A hybrid-power driving system (HPDS) (100, 200) includes an engine, a motor, and a transmission. The HPDS may include a single clutch and the transmission can provide at least five forward speed ratios and can provide for at least one reverse speed ratio. The transmission can include three synchronizers and multiple gearwheels that are used in multiple speed ratios. In addition to a pure engine driving mode and a pure motor driving mode, the HPDS can operate using a hybrid-power driving mode (HDM). In the HDM, the HPDS can provide for shifting of gears without power interruption to the output shaft or half-axles and wheels of a vehicle. In the HDM, the continuous power being output can be achieved by keeping a synchronizer engaged with a gearwheel for two consecutive speed ratios.