This paper aims to propose a novel translational parallel manipulator (TPM) with three degrees of freedom (3-DOF), driven by rodless pneumatic actuators (RPA). The developed parallel manipulator is composed of a fixed base frame, a moving platform, and three sets of parallel kinematic chains. In addition, three identical rodless pneumatic cylinders are employed as the linear actuators of the manipulator. To allow more working space for the manipulator, the RPAs are configured into horizontal positions. A mobility analysis of the parallel mechanism verifies the manipulator to possess three translational degrees of freedom. In this study, a geometric method is introduced to solve the kinematic relation between the actuated joints and the moving platform: A vector-loop closure equation is first established for each limb of the manipulator; by solving the equation, solutions for both the inverse and forward kinematics are obtained. For the control of the 3-DOF TPM, a Fuzzy-PID controller with feedback loops is applied. To improve control precision against nonlinearities and uncertainties in the pneumatic plant, a Back-propagation Neural Network (BPNN) is trained to implement effective pre-compensation. Finally, the real-time experiment is conducted to verify the path tracking control of the three-axial manipulator end-effector.