President Samia Suluhu Hassan last year lifted a ban on most political rallies, which her predecessor John Magufuli had imposed in 2016. She also eased other restrictions on news media and opposition parties.
However, Hassan faced criticism from human rights activists last year after several people were arrested for planning protests over a port management deal.
Wednesday's protest in the commercial capital Dar es Salaam was called by the opposition Party for Democracy and Progress, known as CHADEMA.
CHADEMA says it is impossible to have free and fair elections next year under the current constitution, which was adopted in 1977 when Tanzania was under single-party rule. Protesters also called on authorities to bring down the cost of living.
Thousands of CHADEMA supporters marched through Dar es Salaam waving banners with slogans pushing for an independent electoral body and constitutional reforms. Police officers accompanied the marchers.
"I'm here to push for the new constitution and for the new electoral laws which will bring accountable leaders," Ananilea Nkya, a rights activist and one of the protesters, told Reuters news as she walked.
"I will continue to fight and protest until we get all of these."
CHADEMA is pushing for a new constitution that trims presidential powers and strengthens the independence of the country's electoral body.
Previous attempts to reform the constitution have failed. In 2015, the government cancelled a planned constitutional referendum after the electoral commission said it needed more time to register voters.
Hassan is expected to run for a new term in next year's election.
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