The bill received only 206 votes from MPs and senators, with 473 votes against. Three MPs and three senators abstained from the vote, reports the Bangkok Post.
The bill required 362 votes from the joint chambers, including one-third of the Senate, or 83 senators, to pass the first reading.
It received only three votes of support from senators. They were Naowarat Pongpaiboon, Pisan Manawapat and Monthian Boontan.
Party-list MP of the Democrat Party Panit Wikitset was among the three MPs who abstained.
The bill had the support of more than 135,000 eligible voters and called for key changes in the 2017 constitution. It was sponsored by Internet Law Reform Dialogue, Re-Solution group, the Progressive Movement and the Move Forward Party.
One of the most controversial proposals was to abolish the Senate, leaving only the House of Representatives in parliament.
Supporters of the bill said the Senate was the product of the coup-makers’ National Council for Peace and Order, since dissolved.
Senator Kamnoon Sidhisamarn, spokesman for the Senate whip, argued it would allow MPs to monopolise lawmaking. Senators also denied they were proxies of the coup regime.