Publius Cornelius Cossus was a consular tribune in 408 BC of the Roman Republic. Cornelius belonged to the Cornelia gens, one of the older patrician gens of the Republic. Cornelius father was the Roman hero Aulus Cornelius Cossus who had slewn the King of the Veii, Lars Tolumnius, in single combat. Cornelius had two known brothers, , consul in 413 BC and Gnaeus Cornelius Cossus, consul in 409 BC. Following filiations it would seem that Gnaeus Cornelius Cossus, consular tribune in 406, and , consular tribune in 395 BC, were the sons of Cornelius or his namesake, Publius Cornelius Cossus, consular tribune in 415 BC.