Numerical computations are made of axisymmetric laminar hydrogen jet diffusion flames, focusing on the unsteady behavior under microgravity and the effects of magnetic field. In the computations, multicomponent diffusion and detailed chemical kinetics are considered. In the condition under microgravity without magnetic field, it is revealed that combustion products remain around the diffusion flame because of the lack of natural convection, and that the amount of O2 diffusing to the flame region becomes retarded. That is the reason why the heat release rate in the diffusion flame decreases with the lapse of time. When a gradient magnetic field is added, convection is induced around the diffusion flame by the magnetic field which induces magnetic buoyancy force due to the inhomogeneity of magnetic susceptibility. The flow configuration formed by the magnetic force under microgravity is similar to that under the normal gravity without the magnetic force. The positive gradient of the magnetic field induces the reverse convection which forms the depressed and flattened flame in the normal gravity field. The negative gradient of the magnetic field accelerates the flow together with the normal gravity.