The new members of the National Assembly will be responsible for choosing a successor to 86-year-old President Raul Castro when he steps down next month.
Raul took over in 2006 from his ailing brother Fidel, who had governed since seizing power during the 1959 revolution.
Eight million Cubans are expected to turn out to ratify 605 candidates for an equal number of seats in the Assembly, a process shorn of suspense and unique to the Communist-run Caribbean island nation.
"They're the most important elections of recent years, because we are going to vote for new people who will govern from then on," day-care center guardian Ramon Perez told AFP.
Sunday's general election is the first since the death in 2016 of Fidel Castro, and marks the beginning of major change at the top in Cuba.
Candidates may be either members of the Cuban Communist Party or not, and may also belong to trade unions or be students.
"The designation of candidates is based on merit, abilities and the commitment of the people," Raul Castro said
"Nobody exchanges promises for votes, or boasts of his abilities to get supporters... This is the true and exceptional face of what we proudly call socialist democracy," the official daily Granma wrote.
More than half of the candidates, 322, are women.
Cuba's president is designated by a 31-member Council of State, whose head is automatically president of the country. But the Council of State first has to be selected by the National Assembly.
Castro had already announced that he would not be seeking a new term, although he is expected to remain head of the Communist Party until 2021.
Turnout for the election is expected to be around 90 percent. Although voting is voluntary, not voting is frowned upon and going to the polls is considered an act of sovereignty and of "revolutionary affirmation."