This paper presents the design of a variable stiffness actuator (VSA) using a multi-pulley system with a linear spring. To generate compliance for the VSA, twelve outer and six inner pulleys are evenly arranged around a center and are serially connected to a spring through a cable. The spring gets extended when the inner pulleys rotate about the center. The output stiffness is determined as the derivative of the elastic force exerted on the cable with respect to the time, and it can be varied by adjusting the locations of the inner pulleys. This design employs a cam disk to move the pulleys simultaneously, resulting in a compact design. This paper provides the design concept, theoretical analysis, and numerical examples to demonstrate the proposed VSA and its performance. Through some examples, it is found that the VSA can provide a maximum torque of 30 N-cm with a maximum defection of 40 degrees. These results can present a wide application and high adaptability of the proposed design to various robotic systems and devices.