This paper focuses on developing a pneumatic-driven and horizontal-structure linear delta robot (PH-LDR) and increasing its trajectory tracking performance on the three-degrees-of-freedom (3-DOF) space. With the investigation of inverse and forward kinematics, the parallel mechanism of PH-LDR is designed by using three high-power and low-cost rod-less pneumatic actuators (PAs) to track 3-DOF motion, and this has a horizontal structure to enlarge the workspace. Since the PH-LDR features nonlinear coupling among its three axes and is disturbed by the three high-nonlinear rod-less PAs, the tracking control performance is significantly decreased, subject to uncertain nonlinearity and parametric uncertainty. Therefore, a fuzzy-PID controller is used to achieve highly accurate 3-DOF trajectory tracking, and furthermore, this study exploits neural networks (NNs) to pre-compensate the impacts arising from the compressibility of air and temperature change. The control system for the PH-LDR also features an embedded controller that allows real-time control. Experimental demonstration verifies the developed PH-LDR with the proposed controller, and the dynamic tracking accuracy in 3-DOF trajectory can be achieved.