Cuckoo search algorithm is an efficient random search method for numerical optimization. However, it is very sensitive to the setting of the step size factor. To address this issue, a new cuckoo search algorithm based on cloud model is developed to dynamically configure the step size factor. More specifically, the idea of giving consideration to both fuzziness and randomness of cloud model is innovatively introduced into cuckoo search algorithm, and the appropriate step size factor can be determined according to the membership degree and an exponential function, so as to realize the adaptive adjustment of the control parameter. After that, simulation experiments are conducted on 25 benchmark functions with different dimensions and two chaotic time series prediction problems to comprehensively evaluate the superiority of the proposed algorithm. Numerical results demonstrate that the developed method is more competitive than the other five CS and several non-CS algorithms.