The basic whale optimization algorithm(WOA) has the defects of low convergence, getting easily trapped into local optima, and being difficult to keep balance in exploration and exploitation when solving the shifted functions whose optimum are not at the near origin. A whale optimization algorithm based on cosine control factors and polynomial mutation(CPWOA) is proposed to solve the mentioned defects. In this algorithm, the control parameter is changed as a cosine curve, and a synchronous cosine inertia weight is added to slow down the convergence speed early in the iteration of the algorithme thus improve exploration, and to accelerate the convergence in the later iteration thus improve the accuracy of the exploitation. And polynomial mutation is joined in the optimum whale location to enhance the ability of jumping out of local optimal solutions. By the experiments on multiple shifted benchmark functions such as unimodal, multimodal, and fixed-dimension multimodal, the proposed strategy outperforms the WOA, the EHO, the GWO, the SCA, the MBO and other improved WOAs on solution accuracy and stability. The non-parametric statistical test is carried out to show the significance of the difference of the proposed method.