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Shape memory alloys are a category of smart materials which exhibit large deformations under temperature or magnetic stimuli due to micromechanical changes. These alloys offer a good potential in design of control systems, sensors and actuators due to two main effects called shape memory effect and superelastic effect. Main advantages of these systems are their small scale, low weight, low activation power, long life and high power to weight ratio. On the other hand, the main disadvantage of thermal ones is their low actuation frequency. In this work, inspired by human arm muscles, a new actuator is designed and its actuation time is minimized utilizing the thermoelectric effect. The process requires simultaneous analysis of heat transfer, constitutive equations, phase transformation and also the dynamic equations of the actuator. The dynamic response of the designed actuator is compared with the similar experimental data available in the literature and finally it is shown that, the actuation time of the proposed actuator can be reduced at least 50% thanks to the Peltier effect.