The stacker crane is a long-and-thin structure with a large length-to-width ratio. It is difficult to obtain a topology configuration with good period properties using traditional optimization methods. While the mathematical model of periodic topology optimization - in which the elements' relative densities are selected as design variables, and mean compliance as the objective function - is established. To find a topology configuration with a good period property, an additional constraint condition must be imported into the mathematical model. According to the optimization criteria method, the iterative formula of design variables is derived in the virtual sub domain. To verify the capability and availability of the proposed method, periodic topology optimization of a single-mast stacker crane is investigated in this paper. The results show that configurations with good periodicity can be obtained when the number of sub domains is varied. After considering mean compliance and complexity, the optimal configuration has eight periods. A preliminary lightweight design scheme is proposed based on this configuration of a stacker crane, which is a periodic feature structure.