Haydn Harwood, 33, says the black spiders are in "every nook and cranny" of the outside walls of his house and garage in Llanedeyrn.
He said his wife, Kayleigh, and any family members who visit are afraid of venturing into the garden.
Tube spiders are one of the UK's largest, with bodies up 2.2cm (0.9in), with green iridescence on their jaws.
Mr Harwood first spotted the colony at his end-of-terrace home a year ago.
He said: "They are nocturnal creatures so I hadn't seen them until one night when I was outside having a cigarette because I am not allowed to smoke in the house.
"I saw something move, went in and got a flashlight and saw them all in the cracks of the walls. They were in the eaves, all along the back wall, down the side of the house and under the kitchen window.
"It is a bit of worry for our pets.
"We have two cats and a Chihuahua and it would be terrible if they got bitten by them.
Tube web spiders - Segestria florentina
He asked a friend for help to exterminate them but within three months the colony had returned.
Mr Harwood said he has asked Cardiff council for help.
Experts say the spiders originated in the Mediterranean and north Africa and made their way to Britain on cargo ships.
They believe the spiders are now able survive and spread because of the UK's increasingly mild climate.

The 27-year-old is the first player to join the club since Thomas Christiansen was appointed head coach last week.
The Poland international has previously had spells in his homeland and Germany.
Klich told the club website: "I'm excited to come to England and test myself in the Championship and I can't wait to get going."
Find all the latest football transfers on our dedicated page.

The girl, who suffered "extensive dog bite wounds to her face" in the attack in Stoke-on-Trent, is being treated at Birmingham Children's Hospital.
Her condition is "serious" but not thought to be life-threatening. Her family remain at her bedside.
Staffordshire Police said the dog had been taken to specialist kennels.
Emergency services were called to Pretoria Road in Etruria at 10:20 BST.
Officers said they understood the attack took place in the garden of the property.
West Midlands Ambulance Service said the girl was airlifted for "emergency care and surgery".
"The girl, who was understandably upset, was given pain relief to help ease her discomfort before ambulance staff assessed her nasty wounds and applied dressings."
"Her condition was said to be serious but stable," the ambulance service said.

The 9m (30ft) tall red and blue statue, dubbed the ZiggyZag, was proposed for middle of Brixton, Bowie's birthplace.
The campaign needed to raise £900,000 but had gathered £50,000 in pledges by its four-week deadline, so no funds will be taken from people.
Organisers still hope to create an "appropriate piece of public art".
The proposed site would have been five streets from Bowie's Stansfield Road birthplace and next to Jimmy C's internationally famous Aladdin Sane mural, which has become a focal point for tributes since the artist's death.
The design team behind the project, This Ain't Rock'n'Roll, said thousands of pounds was pledged within hours of the launch of the campaign in February.
"If someone had told us a year ago that we'd raise £50,000 from nearly 700 wonderful people in just three weeks we wouldn't have believed it possible," a statement from the group said.
"Thank you from the bottom of our Bowie-obsessed hearts for supporting us."
"Of course, £50,000 doesn't go anywhere near realising the ambitions of the ZiggyZag," they added.
"It will be no surprise to anyone that this crowdfund isn't going to hit its target."
But the statement added: "We are still determined to celebrate David Bowie, in Brixton, with a challenging and appropriate piece of public art.
"We're just going to have to approach the fundraising in a different way."
The proposed memorial took its inspiration from the cover art on Bowie's sixth album, Aladdin Sane, which was released in 1973.
It had the support of Lambeth Council, which began discussing the possibility of a permanent memorial with Bowie's family in 2016.
Hundreds of green-fanged tube web spiders have taken over the back garden of a family home in Cardiff.
[NEXT_CONCEPT]
Leeds United have signed FC Twente midfielder Mateusz Klich for an undisclosed fee on a three-year deal.
[NEXT_CONCEPT]
A six-year-old girl is undergoing surgery after being attacked by a Staffordshire bull terrier, police have said.
[NEXT_CONCEPT]
Plans to create a huge lightning bolt memorial to David Bowie in south London have been scrapped after a crowdfunding campaign fell short of its target.