Dr. Francisco Epigmenio Luna Kan (born 3 December 1925) is a Mexican politician. Francisco Luna Kan was governor of the state of Yucatán from 1976 to 1982.

Born in Mérida, Yucatán, he was a practicing doctor of medicine then taught as a Professor of Medicine before his first political offices, first overseeing the state's rural medical system.

Francisco Luna Kan was the first person of Maya ancestry govern Yucatán since the Spanish conquest of Yucatán. For centuries the political elite had been Yucatecos of Creole Hispanic decent. It was widely said that party officials of Mexico's ruling Partido Revolucionario Institucional (PRI) took the unusual step of selecting a person of Maya decent as their candidate in 1975 because the opposition Partido Acción Nacional (PAN) had been getting many votes in Yucatán, and PRI candidates had been getting a poor showing in the state's predominantly Maya towns and villages. It was said that PAN got the majority of votes in the previous governor's race, and the PRI managed to maintain control of the state only through fraud in counting votes.

Shortly after his election Luna Kan was subjected to an unpleasant incident while taking a train to Mexico City for a governmental conference. Luna Kan was thrown off the train, as the railroad conductors thought it inconceivable that this short man of obvious Native American features was telling the truth when he claimed to be a state governor.

After his term as governor Luna Kan resigned from the PRI and joined the Partido de la Revolución Democrática (PRD). He unsuccessfully ran as that party's candidate for mayor of Mérida in 1998. As of 2004 Francisco Luna Kan holds a seat in Mexico's Cámara Federal de Diputados as a PRD deputy for Yucatán.