The election frontrunner is Keiko Fujimori, daughter of former President Alberto Fujimori, who cracked down on the Maoist Shining Path guerrillas.
However she is not expected to win a clear majority.
Opinion polls indicate that she will not obtain the 50% of votes needed to avoid a second run-off round.
Her closest challengers are centrist Pedro Pablo Kuczynski and left-winger Veronika Mendoza.
Shadow of jailed ex-president cast over Peru polls
Keiko Fujimori has marketed herself as being tough on crime and is supported by some Peruvians who credit her father with defeating the rebels.
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