A multi-mode continuously variable transmission with both speed coupling and torque coupling includes an engine-power input assembly, a hydraulic transmission assembly, a motor transmission assembly, a planetary gear assembly, an output member, a clutch assembly, and a brake assembly, wherein an output end of the planetary gear assembly is connected to the output member, the clutch assembly connects the engine-power input assembly, the hydraulic transmission assembly, and the motor transmission assembly to an input end of the planetary gear assembly, and the clutch assembly connects the engine-power input assembly to the hydraulic transmission assembly; and the clutch assembly and the brake assembly provide a continuously changing transmission ratio between the engine-power input assembly or/and the motor transmission assembly and the output member.