A recently developed computational scheme, based on the complex-rotation method combined with a mixed Slater-Landau basis expansion, has been applied to calculations of photoionization from atomic hydrogen ground and excited states in a strong magnetic field typical of magnetic white dwarf stars. Photoionization cross sections are presented for the twelve states, 1s_0_, 2s_0_, 2p_0_, 2p_-1_, 3s'0, 3p_0_, 3p_-1_, 3d'0, 3d_-1_, 3d_-2_, 4f_-2_, and 4f_-3_, with magnetic field strengths from 23.5 to 2350MG.