It began in November but 20 cases have been notified in the last week and the total is more than for the whole of Wales in the last three years.
So far, 32 secondary schools, primary schools and nurseries are affected.
Parents are being urged to make sure their children receive the measles, mumps and rubella (MMR) vaccination.
The outbreak only affects the Abertawe Bro Morgannwg University Health Board area and eclipses the number of cases across the whole of Wales since 2010.
Last year's figure of confirmed cases for Wales stood at 116, while there were just 19 in 2011 and eight the year before, according to Public Health Wales.
There were 159 cases in 2009, still lower than the current outbreak in south west Wales.
Dr Marion Lyons, director of health protection for Public Health Wales (PHW), said: "We continue to be concerned at the number of cases of measles we are seeing in the Swansea and Neath Port Talbot areas.
"We cannot emphasise enough that measles is an illness that can kill, or leave patients with permanent complications including severe brain damage, and the only protection is two doses of the MMR vaccination."
She added that people most at risk of catching measles are children of school age who have not had two doses of MMR.
Children should receive the first dose of the vaccine at 12 to 13 months of age and the second at three years and four months of age
PHW estimates there are more than 8,500 school children at risk of measles in the Abertawe Bro Morgannwg area.
Many people who catch measles will have a fever, cough, red eyes, and blocked nose and feel generally unwell.
The blotchy rash appears a few days later beginning on the face and spreading downwards to the rest of the body over several days.

A lady was knocked over during the theft in Market Street, Limavady, which happened at about 15:00 BST on Friday. She suffered non life-threatening injuries.
Police have said the officers were nearby when the incident occurred and a 20-year-old man was detained.
Supt John Magill commended the off-duty officers.
"I feel that this is a perfect example of police officers continuing to keep people safe, whether they are on or off duty at the time."

All 10 had their passports confiscated after they were detained at Montreal's Trudeau International Airport at the weekend.
Police said in a statement on Tuesday that none of the suspects had been charged, but investigations were ongoing.
Their families have been informed.
"These are very difficult times for the relatives and loved ones of the persons arrested, as the decision to leave the country was not that of the family, but of a single family member," the statement said.
"As a result, family members often find themselves at a complete loss and unable to understand the decision made by the youth."
Police said they could not disclose the identity of the suspects or provide information about what led to their arrests.
Steven Blaney, Canada's public safety minister, commended the officers for their "continued vigilance" in protecting communities from "the ongoing global terror threat".
Canadian troops are part of a multinational coalition to halt the advance of IS militants in Iraq and Syria.
Prime Minister Stephen Harper announced in March that he planned to expand the mission and has since pledged $139m (Â£89m) to help alleviate the growing humanitarian crisis in the region.
An outbreak of 189 cases of measles has been reported in Swansea, Neath and Port Talbot, Public Health Wales says.
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Two off-duty police officers have arrested a man after a burglary at a shop in County Londonderry.
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Ten youths have been arrested by Canadian police on suspicion of planning to travel to Iraq and Syria to join Islamic State.