The invention discloses a continuous-power-shifting two-gear speed changing box which comprises a speed changing box body, a power input shaft, a power output shaft, a slow-gear transmission chain and a rapid-gear transmission chain. The rapid-gear transmission chain is of a clutch structure, the slow-gear transmission chain is provided with an overrun clutch, the overrun clutch conducts overrunning when the rapid-gear transmission chain is in joint transmission, the power output shaft is in transmission fit to output power to a differential mechanism, according to the two-gear speed changing box, the output power of a power device is not required to be cut off, the switching between the slow gear and the rapid gear can be directly conducted, the power output of the power device is kept and matched with the running road condition, the jerking sense is reduced, controllability is improved, the driving comfort of a motor vehicle is improved, the power device can stably run for a long period, the service life of the power device is prolonged, and driving energy resources are saved. Further, the joint between the gears is smooth and stable, power consumption in climbing is reduced, power of the power device is fully utilized on the flat ground, driving and gear shifting of the motor vehicle are more stable and smooth, and the aims of saving energy, being environmentally friendly and reducing the use cost are achieved.