Conventional state-space model predictive control requires a state estimator/observer to access the state information for feedback controller design. Its drawbacks are the numerical convergence stability of the observer and closed-loop control performance deterioration with activated plant input/output constraints. The recent direct use of measured input and output variables to formulate a non-minimal state-space (NMSS) model overcomes these problems, but the subsequent controller is too sensitive to model mismatch. In this article, an improved structure of NMSS model that incorporates the output-tracking error is first formulated and then a subsequent predictive functional control design is proposed. The proposed controller is tested on both model match and model mismatch cases for comparison with previous controllers. Results show that control performance is improved. In addition, a linear programming method for constraints dealing and a closed form of transfer function representation of the control system are provided for further insight into the proposed method.