There has been a high turnout at voting stations, reports say.
Opinion polls have put the ruling Chama Cha Mapinduzi (CCM) party ahead, but the result is expected to be close.
Four opposition groups are backing one candidate, a former prime minister, in the presidential race.
Some of the major issues for the almost 23 million registered voters include access to clean water, improved health care and better education.
President Jakaya Kikwete, who is standing down after two terms, has called for peace ahead of the election, adding that “anyone who tries to cause trouble will be dealt with”.
The CCM was formed in 1977 from a merger of two post-colonial parties and has effectively been in power since independence in 1961.
Tanzania’s works minister, John Magufuli, 55, has promised change and to improve on the pace of progress laid down by the previous CCM government.
John Magufuli has promised to end the country’s power shortages and exploit Tanzania’s natural gas discoveries.
“My government will put emphasis on fighting corruption, job creation and industrialization,” he said on October 24.
John Magufuli is nicknamed The Bulldozer for driving a program to build roads across Tanzania.
Ukawa coalition’s candidate Edward Lowassa, 62, decided to leave the CCM when it did not pick him as its presidential candidate earlier this year. Four opposition parties rallied behind Edward Lowassa as a coalition candidate.
“We must stop being a nation of beggars,” he told a rally on October 24.
“It is a shame for Tanzania to still be poor after 54 years of independence.”
Edward Lowassa has already served as prime minister, but had to resign over a corruption scandal in the energy sector. He continues to deny involvement in the scandal.
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