To align a pair of optical fibers, it is required that the micro actuators used be small and have the characteristics of high accuracy and fast response time. A trapezoidal piezoelectric bimorph actuator was proposed for pushing and pulling an optical fiber. Based on a mathematical model and finite element model established in this paper, we analyzed the output displacement and output force of the proposed trapezoidal piezoelectric actuator under the influence of structural parameters. Since the piezoelectric bimorph actuator had a hysteresis effect, we applied particle swarm optimization to establish a Prandtl-Ishlinskii (PI) model for actuator and parameter identification. Then, two control methods, namely feedforward control considering hysteresis effects and fuzzy proportional-integral-derivative (PID) control employing feedback, were proposed. Finally, a composite control model combining the two control methods with fewer tracking errors was designed. The results show that the output displacement of this actuator is larger than that of a rectangular one. Additionally, the fuzzy PID control has a lower response time (15 ms) and an overshoot (5%).