We systematically investigate the equilibrium shapes of droplets deposited on a set of chemically striped patterned surfaces by using an Allen-Cahn-type phase-field model. Varying the widths of the stripes d, the volume V, as well as the initial positions of the droplets, we release the droplets on the top of the surfaces and observe the final droplet shapes. It is found that there are either one or two equilibrium shapes for a fixed ratio of d/V-1/3 and each equilibrium shape corresponds to an energy minimum state. The aspect ratio of the droplets xi shows a periodic oscillation behavior with a decreasing amplitude as d/V-1/3 decreases, similar to the stick-slip-jump movement of a slowly condensing droplet on a chemically striped patterned surface. Additionally, by comparing the movements of slowly evaporating and condensing droplets, we have observed a hysteresis phenomenon, which reveals that the final shapes of droplets also rely on the moving paths. Through modifying the dynamic contact angle boundary condition, the contact line movements of droplets under condensation and evaporation, which are far from equilibrium, are addressed.