The invention discloses a mechanical transmission and a control method for the mechanical transmission. The mechanical transmission comprises an input shaft, a first meshing sleeve, a second meshing sleeve, a clutch, an odd number gear output shaft and an even number gear output shaft. A power transmitting route is composed of the clutch, the first meshing sleeve, the second meshing sleeve, the odd number gear output shaft and the even number gear output shaft. By orderly controlling engagement and disengagement of the clutch and meshing and separating of the first meshing sleeve and the second meshing sleeve, the power of the input shaft can be alternately transmitted to the odd number gear output shaft or the even number gear output shaft, so that the up-shift operation and the down-shift operation are achieved. The gear shifting operation is achieved through matched operation of the clutch and the first meshing sleeve and matched operation of the clutch and the second meshing sleeve. Therefore, the number of clutches in the prior art is reduced, the size of the transmission is reduced, meanwhile, the dragging resistance caused by the clutch of the prior transmission is lowered, the transmission efficiency is improved, and the production cost of the whole mechanical transmission is lowered.