The pneumatic artificial muscles (PAMs) have been extensively used in various robotic applications despite of their highly nonlinear behavior. However, precise positioning control of a PAM remains to be a difficult problem although several decades have passed since its introduction to the field. The present article tries to synthesize a nonlinear contraction length controller of a McKibben PAM. We applied the backstepping algorithm to a three-element model to determine a feedback control structure for contraction length control of a PAM. We then introduced a radial basis function (RBF) neural network for compensation of nonlinearities that resided in the tracking error dynamics. Numerical simulation has been conducted for a sinusoidal reference trajectory of the actuator to demonstrate improved tracking performance of the proposed controller over the conventional PID controller.