In this paper, the propulsive performance of a caudal peduncle-fin swimmer mimicking a bio-inspired robotic fish model is numerically studied using a fully coupled FSI solver. The model consists of a rigid peduncle and a flexible fin which pitches in a uniform flow. The flexible fin is modeled as a thin plate assigned with non-uniformly distributed stiffness. A finite volume method based in-house Navier-Stokes solver is used to solve the fluid equations while the fin deformation is resolved using a finite element code. The effect of the fin flexibility on the propulsive performance is investigated. The numerical results indicate that the compliance has a significant influence on the performance. Under the parameters studied in this paper, the medium flexible fin exhibits remarkable efficiency improvement as well as thrust augment, while the least flexible fin shows no obvious difference from the rigid one. However, for the most flexible fin, although the thrust production decreases sharply, the efficiency reaches the maximum value. It should be noted that by non-uniformly distributing the rigidity across the caudal fin, our model is able to replicate some fin deformation patterns observed in both the live fish and the experimental robotic fish.