High-temperature deformation around the glass transition temperature Tg and the dynamic mechanical behavior of La30Ce30Al15Co25 metallic glass were investigated. According to dynamic mechanical analysis (DMA) results, La30Ce30Al15Co25 metallic glass exhibits a pronounced slow β relaxation process. In parallel, strain-rate jump experiments around the glass transition temperature were performed in a wide range of strain rate ranges. The apparent viscosity shows a strong dependence on temperature and strain rate, which reflects the transition from non-Newtonian to Newtonian flow. At low strain or high temperature, a transition was observed from a non-Newtonian viscous flow to Newtonian viscous flow. It was found that the activation volume during plastic deformation of La30Ce30Al15Co25 metallic glass is higher than that of other metallic glasses. Higher values of activation volume in La30Ce30Al15Co25 metallic glass may be attributed to existence of a pronounced slow β relaxation. It is reasonable to conclude that slow β relaxation in La30Ce30Al15Co25 metallic glass corresponds to the “soft” regions (structural heterogeneities) in metallic glass.