Aaron Lewis, 26 and from Toxteth, was shot three times outside Anna Jungs in Grosvenor Road, Wavertree at about 19:00 GMT on Wednesday.
He was taken to Aintree Hospital, where he was later pronounced dead.
Merseyside Police believe the offender ran down the road towards the city centre and said the shooting was related to organised crime.
Officers said Mr Lewis was known to them.
At about 19:40, a 19-year-old man went to hospital with a gunshot wound to his upper body.
His condition is not thought to be life-threatening and detectives believe he had been with Mr Lewis.
The latest death follows the fatal shooting of Thomas Baker at Stanley Meat Market in Old Swan on Friday and highlighted a "serious escalation" of gang violence in Liverpool, police said.
Police said that while both deaths were related to serious and organised crime, the shootings were not linked.
In addition to Mr Baker and Mr Lewis, Mark Hillman and Blake Brown have been killed in the city.
A police spokesman said gun crime had increased in recent months after falling year on year from 2013 to 2016.
Since April, 78 firearms have been discharged, 18 more than in the whole of the previous 12 months.
An increasing number of new guns are being used, the spokesman added, and officers do not know how or where gangs are obtaining them.
Police said the majority of shootings this year were linked to organised crime and the victims will not co-operate with officers.
Liverpool Mayor Joe Anderson and Wavertree MP Luciana Berger have joined forces with Merseyside Police to appeal for public help.
Ms Berger said: "We as a community need to work together to help end this violence on our streets."
Mr Anderson said: "By coming together as a city we can send out a powerful message to the perpetrators that they will be found and... punished."
A series of warrants are being executed across Liverpool as part of a planned crackdown on gun crime, but no weapons have been recovered.

The 4.4-metre-long (14-ft) cloth is on show until 24 June.
Viewings are free but must be booked. One million people have already signed up.
Some devotees believe the shroud is the burial cloth of Jesus Christ. Sceptics point to carbon dating that suggests it is a medieval forgery from the 1300s.
Scientists have not agreed on how the image of a man was imprinted on the cloth.
Turin Shroud: See it in detail
Pope Francis will be among those to view the shroud, during a visit to the northern Italian city on 21 June.
The last public viewings were in 2010, when 2.5 million people came to see it.
The Church has not officially claimed that Christ's body was wrapped in the shroud, preferring instead to focus on what it means to those who see it.
"Whether you believe or don't believe, there is no doubt it is something special," an Italian man who was among the first visitors on Sunday told the AFP news agency.
Earlier this week, Archbishop of Turin Cesare Nosiglia said: "What counts the most is that this shroud... reflects in a clear and precise manner how the gospels describe the passion and death of Jesus.
"It is not a profession of faith because it is not an object of faith, nor of devotion, but it can help faith."
Archbishop Nosiglia said that many of those coming to see the shroud would be returnees.
"That means there is a fundamental need in people's hearts to renew this incredible experience that they had the first time they saw it," he said.
"Even non-believers will come. It's an occasion that brings everybody together."
The shroud is displayed in a climate-controlled case for 12 hours a day in Turin's Cathedral of St John the Baptist.
A man has been shot dead in a "cold-blooded, targeted attack" outside a Liverpool chip shop, police said.
[NEXT_CONCEPT]
The Turin Shroud has gone back on public display in the Italian city's cathedral, after a break of five years.