Selection of useful bands plays a very important role in hyperspectral image classification. In the past decade, metaheuristic algorithms have been used as promising methods for solving this problem. However, many metaheuristic algorithms may provide unsatisfactory performance due to their slow or premature convergence. Therefore, how to develop algorithms well balancing the exploration and exploitation, and find the suitable bands precisely is still a challenge. In this paper, a new hybrid global optimization algorithm, which is based on the Wind Driven Optimization (WDO) and Cuckoo Search (CS) is proposed to solve hyperspectral band selection problems. Both WDO and CS have strong searching ability and require less control parameters, but easily suffer from premature convergence due to loss of diversity of population. The proposed approach uses the Chebyshev chaotic map to initialize the population at initial step. The population is divided into two subgroups and WDO and CS are adopted for these two subgroups independently. By division, these two subgroups can share suitable information and utilize each other’s pros, thus avoid premature convergence, and obtain best optimal solution. Furthermore, the Levy flight step size in CS algorithm is adaptively adjusted based on fitness value and current iteration number, which helps in boosting the convergence speed of algorithm. The experimental results on three standard benchmark datasets namely, Pavia University, Botswana and Indian Pines, prove the superiority of the proposed approach over standard WDO and CS approaches as well as the other traditional approaches in terms of classification accuracy with fewer bands. © 2020, Springer Science+Business Media, LLC, part of Springer Nature.