The party was founded in 1986 when M. V. Raghavan was expelled from the CPI(M) due to a grave difference of opinion regarding the formation of alliances with the IUML.

His support for forming a united front with parties such as the Indian Union Muslim League in order to take on alliances led by the INC was ultimately rejected by the CPI(M) leadership.

[1][2] In 2011 assembly election of Kerala, CMP fielded 3 candidates but could not win any seat.

CMP had links with the Party of Democratic Socialism of Saifuddin Chaudhury in West Bengal.

CMP participated in the Confederation of Indian Communists and Democratic Socialists.