In edge plasma, hydrogen molecules have considerably high density. The vibrational distribution of hydrogen can be changed via collisions with plasma. In this paper, various processes of hydrogen molecules are discussed and newest cross section data are adopted while the unavailable data are calculated by semi-classical Gryzinski method. Based on the quasi-stationary approximation and the quasi-steady collisional-radiative model, the vibratioanl distribution of hydrogen in low temperature are studied. The results show that at lower vibrational level, the distribution decreases with the increase of electron temperature when the electron temperature is less than 10 eV. On the other hand, the distribution presents an opposite trend at high vibrational level.