This paper proposes a vibration controller for overhead cranes considering limited horizontal acceleration. Our previous article proposes a transfer-function-based vibration controller that suppresses the vibration of a lifted load regardless of wire length. However, this controller does not consider the nonlinear acceleration limitation of the crane. Thus, to consider the limited acceleration with a transfer-function-based controller, a linear parameter varying (LPV) acceleration-limitation model is developed. Moreover, the proposed controller is designed by using a dynamic model of the crane and the LPV limited-acceleration model. Experiments verify that the proposed controller suppresses the vibration and does not exceed the acceleration limits.