In this paper, we choose a pneumatic soft actuator with a bellow shape(pneumatic bellow actuator) as the object, and propose a model-free tracking control method based on the broad learning system to realize its trajectory tracking control. We first introduce the structure of the pneumatic bellow actuator and the working principle of the experimental platform. Based on the real-time position information of the actuator, we propose a tracking control method based on the broad learning system. Inspired by the integral term in PID tracking control methods, we not only use the system tracking error as one of the inputs of the broad learning system, but also use the integral term of the tracking error as another input to eliminate the constant deviation between the desired and the actual trajectory. Then, we utilize the broad learning system to calculate the control pressure, and we adjust the weight of the broad learning system online by the learning law based on the gradient descent method to reduce the tracking error. Experiments are designed to verify the effectiveness of the proposed method. The proposed method does not need to establish a model and simplifies the controller design steps. Compared with the control methods based on the deep neural network, the proposed method can achieve higher tracking control accuracy without excessive computation.