To simulate the complex and continuous undulation of fishtail in nature, the method of adopting the discrete Multi-Joint mechanism requires a certain number of degrees of freedom, which results in the complexities of mechanism and control necessarily. Compared with Multi-Joint, flexible tail is a better scheme due to continuum, robustness, and simpler control. Hence, this paper proposes a wire-driven elastic robotic fish with flexible tail, which simulates fish muscle through multi-wire drive and adopts a fishlike spine design based on elastic component. Due to these distinctive designs, our robotic fish not only realizes the compliant simulation of fishlike swimming gait, but also owns higher bionic degree. Further, the kinematics model and speed estimation model of the wire-driven elastic robotic fish are developed, and the error between the body wave and the desired fishlike swimming gait is further optimized so as to determine the appropriate parameters of central pattern generator. The results show that the optimized body wave of fishtail matches well with the desired fishlike swimming gait and the RMSE of the stable swimming speed between simulations and experiments is 0.045 m/s, which validates the proposed model and optimization method. Finally, the relationships between the frequency and swimming speed under small amplitude are explored, from which we find that amplitude has a greater impact on speed than frequency at high frequency, and the maximum swimming speed of about 0.54 m/s, i.e., 1.02 BL/s, is obtained.