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Pectoral fins play an important role in the fish swimming performance, especially in maneuverability underwater. This paper presents the swimming propulsion by means of a flexible and lightweight pectoral fin inspired by a Koi Carp. The fin is driven by embedded shape memory alloy (SMA) wires. In this paper, the kinematics of a pectoral fin from a live Koi Carp fish is first studied. The motion of fin rays is analyzed, in which four basic patterns are extracted from the motion of the pectoral fin captured experimentally, especially the motion in retreating and hovering. Inspired by the fin motion of the live fish, an SMA-driven fin ray providing a two-degree-of-freedom bending motion is proposed. The detailed design of the bioinspired pectoral fin driven by SMA-driven rays is then presented. The basic unit is an SMA-driven plate with two SMA wires embedded on the two opposite sides of a plastic plate. The SMA-driven plate can bend by a pulse width modulation current delivered through SMA wires. An assembled SMA fin ray is next formed by two SMA plates, which are placed in series with their cross sections perpendicular to each other. As a result, a lightweight bioinspired pectoral fin is constructed by placing radially multiple SMA fin rays. The integrated pectoral fin is able to exhibit four patterns extracted in the biological kinematic study. The simulation and experimental optimization on the SMA-driven plate are presented in the final part of this paper. The diameter of SMA wires is optimized and the oscillation angle of SMA plate is obtained. The experiment is also conducted to evaluate the motions of the bioinspired pectoral fin. The result demonstrates that the SMA-based fin is effective in driving the bioinspired fin. Moreover, the bioinspired pectoral fin is able to perform complex motions that can contribute to the maneuverability of fish robots.