Flames in an O-2-containing atmosphere rely on natural or forced convection to replenish reactants and remove hot products. Because natural convection is absent under microgravity, diffusion flames become spherical, have low power, and eventually are extinguished. This paper deals with a simple method of generating convective air flows on the application of magnetic fields and supporting combustion under microgravity conditions. Magnetic fields, which act on paramagnetic oxygen, attract fresh air rich in O-2 and push out the combustion products. Thus, a diffusion flame in air was quenched after a few seconds under microgravity. However, when compact permanent magnets were installed, this diffusion flame became more brilliant and shorter than with normal gravity and continued to burn without changing its shape or luminosity during 10 sec of microgravity. Large soot particles, which are characteristic under microgravity, disappeared. These experiments demonstrate that magnetic fields induce air flows and support combustion completely with microgravity. The present method will also be useful to burn liquid or solid fuel under microgravity without forced convection by compressors.