β decay in the strong magnetic field of the crusts of neutron stars is analysed by an improved method. The reactions 67Ni(β-)67Cu and 62Mn(β-)62Fe are investigated as examples. The results show that a weak magnetic field has little effect onβ decay but a strong magnetic field (B ＞ 1012G) increases β decay rates obviously. The conclusion derived may be crucial to the research of late evolution of neutron stars and nucleosynthesis in r-process.