This paper aims to understand influence of the obliquity of fin ray on its motion performance. An environment-friendly propulsion system mimicking undulating fins of stingray had been built. Investigations were presented by using three-dimensional unsteady Computational Fluid Dynamics (CFD) method. An unstructured, grid-based, unsteady Navier-Stokes solver with automatic adaptive remeshing was used to compute the unsteady flow around the fin through twenty complete cycles. The pressure distribution on fin surface was computed and integrated to provide fin forces which were decomposed into lift and thrust. Vortex contour maps of the fin with different obliquity of fin ray were displayed and compared. Finally, we draw a conclusion that the generated propulsion force of the biomimetic propulsor is gradually increase with the obliquity of the fin ray from 0 degree till a certain angle and then gradually decrease with the obliquity of the fin ray from the certain angle till 90 degree. The results provide valuable information for the optimization of robotic underwater undulating propulsor design.