We proved a classification theorem of admissible irreducible mod p representations in terms of supersingular representations. In the proof, a pro-p-Iwahori Hecke algebra has an important role. I will talk about some relations between mod p representations and modules of pro-p-Iwahori Hecke algebra. Some parts of the talk are based on joint works with F. Herzig, G. Henniart and M.-F. Vigneras.