Shape memory alloys (SMAs) are smart materials that change their crystalline structures when subjected to heat or tension, resulting in a macroscopic deformation. When applied to actuators, SMAs present a remarkable load–weight ratio and flexibility, making them suitable for diverse applications. However, challenges such as their energy consumption, nonlinear control, and low displacement must be considered. This paper presents a new strategy for improving the total displacement while adding neither supplementary SMA wires nor complex external devices. In addition, a novel control strategy is proposed to improve the nonlinearity of SMAs’ behavior. A hoist system was developed to linearly increase the displacement with the number of pulleys and wire turns used. The design also used parallel actuation to increase the load capacity. The actuator presented a high load capacity with reduced weight, lifting more than 100 times its own mass, with a low-cost and robust external system. The simplicity of the actuator’s control and production and its lightness make it a suitable option for a wide range of applications, including wearable exoskeletons.