Abstract The crystal structure of solid hydrogen under high pressure has been extensively investigated using first-principles density functional calculations. We discussed the impact of two pseudopotentials (ultrasoft pseudopotential and norm conserving pseudopotential) with/without Van der Waals force on hydrogen system, and conducted a series of geometry optimization on 11 structures (C2, P63/m, Pca21, C2/c, Cmca, Cmca-12, P63/mmc, P21/c, C2/c-1, Pbcn, and Pa3), which was obtained by referring to literature, finally we got four reasonable phase transition sequence of crystal hydrogen(Cmca-12, Cmca, Pca21, and P63/m). The transition pressures of four cases are different. We also calculated the vibrational Raman/IR spectra of the four sequences of which the enthalpies are nearly equal and it can provide guides to experiment.