Abstract In the design of a wind farm, the placement of turbines is an important factor that affects the efficiency and profit, but automatic placement of turbines is still a challenging problem. This study reveals the “submodular” property of the wind turbine positioning problem based on Jensen wake model. Based on this property, a “lazy greedy” algorithm is used to optimize the placement. This method can obtain solutions with theoretical guarantee of quality. It can also estimate the lower bound of the optimal value of the objective function. This method is tested on three types of wind scenarios. Compared to previous research, this algorithm takes much less time, and always gains a better solution. To enlarge the application scope, the wake model is extended to the large scale complex terrain in this study. The present algorithm and some other algorithms are tested in the simulation of the complex terrain. The experimental results demonstrate the present method’s superior performance.