We have measured the temperature dependence of the electron attachment reaction rate of atomic hydrogen (H) on a liquid 4He surface in applied magnetic fields of 0-5 T at 0.2-0.6 K. The measured surface state electron (SSE) losses are faster at lower temperatures for a given magnetic field. This behavior can be qualitatively understood, since the surface coverage of adsorbed H is large at low temperature and the collisions between H and SSE are frequent. However, the reaction is faster than expected based on the collision frequency argument. The measured reaction rate coefficient K e is strongly temperature dependent. We observe that, as the temperature is lowered, Ke increases by several orders of magnitude. This indicates that some additional effect enhances electron attachment at low temperature. We discuss a possible reaction mechanism between H and SSE.