In order to solve optimal shape design problem arising from fluid dynamics, an optimality criteria (OC) coupled adaptive mesh refinement algorithm has been presented in this paper. The objective is to minimize the dissipated power in the fluid, subject to the Stokes problem as the state equations. By this method, higher resolution of the interface can be obtained with a minimum of additional expense. A material distribution information based indicator is adopted during the automatic local adaptive mesh refinement process. Although only considered the Stokes problem in this study, the proposed method can be applied to a wide range of optimal shape or topology design problems in fluid dynamics.