This paper discusses the modeling and control of the ionic polymer-metal composite (IPMC) actuators which have many promising applications in biomechatronics. A novel mathematical model in continuous-time domain of the IPMC actuator, being a stable second-order dynamical system preceded by a nonlinear hysteresis representation, is proposed. An adaptive controller is formulated for the IPMC actuator based on the proposed model. The proposed adaptive control law ensures the global stability of the controlled IPMC system, and the position error of the IPMC actuator can be theoretically guaranteed to converge to zero. The effectiveness of the proposed model and the superiority of the proposed control to the traditional proportional-integral-derivative control are verified by experimental results.