We investigate the quantum-mechanical transmission of electrons in a four-terminal quantum waveguide (FTQW) subjected to an inhomogeneous magnetic field perpendicular to the FTQW plane with the use of the mode-matching technique. An electron incident through one channel of the waveguide can travel into the other three channels in the quantum ballistic regime. The results show that in zero field the transmission coefficients in two channels perpendicular to the main wire are of similar behavior, but different from that of the channel parallel to the main wire. However, in an applied magnetic field, the transmission coefficients in two channels perpendicular to the main wire exhibit quite difference from each other and depend sensitively on geometric parameters. When different magnetic configurations are applied in the structure, the transmission exhibits various patterns such as step drop, wide valley, sharp peak, and so on. Our results show that one may control the transmission property of the FTQW to match practical requirements in devices by adjusting magnetic configurations or structural parameters.