The ionization processes in collisions of H (1s) atoms with He2+ are studied by the classical trajectory Monte Carlo method. The first-order differential cross sections for ionization are calculated for different field strengths of both transverse and parallel magnetic field, and they increase obviously with the fields applied. Instead of monotonic decline, a peak appears for the differential cross section, with the fields applied. According to the analysis of trajectories, the ionization mechanisms become quite different. In this paper, the influences the strength and direction of the applied field including the incident energy on the ionization mechanisms are also explained.