He said in a speech to Congress this would also involve shortening the term of the legislature. As it stands, general elections are scheduled for July next year.
Vizcarra's proposal comes with Peru's executive and legislative branches locked in a massive power struggle.
The president said his idea would need to be passed by the opposition-controlled legislature, and then approved in a referendum.
"The voice of the people must be heard," Vizcarra told lawmakers, as some cheered him and others yelled insults, in a session on Peru's national day.
"Peru is screaming out for a new beginning," Vizcarra said.
If Congress agrees to the president's proposal, the referendum will be held at the end of the year and the elections "on the second Sunday of April 2020," Justice Minister Vicente Zeballos said.
Shaken by a string of high-profile corruption scandals, Peruvians overwhelmingly approved Vizcarra's anti-corruption reforms in a December referendum.
But he has repeatedly clashed with Congress, which is dominated by the Popular Force party of Keiko Fujimori, who is herself in prison pending trial on corruption charges linked to Brazilian construction giant Odebrecht.
Vizcarra had originally threatened to dissolve Congress and force new legislative elections in June, unless lawmakers backed his anti-graft proposals.
He won a vote of confidence in Congress at the time, and the government was expected to begin negotiations with the opposition over introducing the reforms.
The reforms ranged from campaign finance, to limiting immunity from prosecution that lawmakers enjoy, and blocking those convicted in court from seeking office, as the South American nation of 33 million sought to emerge from the shadow of Latin America's biggest graft scandal.
The proposal to lift legislative immunity turned into the source of the latest conflict between Peru's executive and legislative branches; Vizcarra proposed giving the Supreme Court power to decide whether to strip a legislator of the protection.
Congress, which currently holds the power to lift judicial immunity, rejected the idea.
Vizcarra's proposal to move up elections was met with praise from businesses and analysts, as well as leftist members of Congress, but his opponents accused him of creating too much uncertainty in the government.
"The president is looking to shake up Congress, because there has been no improvement in investment or development in the country," said Fujimori-allied congresswoman Cecilia Chacon.
"The president has nothing to show the people, so he has created a media show to keep getting air time," she argued.
- Odebrecht scandal -
Under Peru's constitution, Vizcarra cannot run in the next election. He has said several times that he would not seek to do so.
Vizcarra, who was vice president to his predecessor Pedro Pablo Kuczynski, rose to power from relative obscurity 16 months after Kuczynski's resignation, when the latter was forced out in 2018.
Kuczynski, who is 80 and underwent heart surgery in May, is being held under house arrest over accusations of money laundering.
Peruvian prosecutors opened an investigation into Kuczynski in June 2018 for his alleged involvement in the sprawling Odebrecht scandal, in which the construction giant paid hundreds of millions of dollars in bribes across Latin America to secure huge public works contracts.
The investigation also looked into two other former presidents, Alejandro Toledo and Alan Garcia.
Garcia committed suicide in April after police arrived at his house to arrest him for money laundering.
Toledo was arrested in the United States in July to face extradition charges to Peru, but remains in US custody.
A fourth former president, Ollanta Humala and his wife Nadine Heredia were indicted in May for allegedly laundering assets.
On July 24, Peru's Supreme Court said it will decide in August whether to free Keiko Fujimori, accused of accepting $1.2 million in illicit party funding from Odebrecht, from pre-trial detention.