The acceleration control schedule (ACS) is crucial in determining the acceleration performance of an aero-engine and is usually acquired by optimization means. To reduce the computational burden in optimizing ACS and improve the ACS superiority, a local receding-horizon optimization method with the structure of model predictive control is proposed. Moreover, a novel online data-driven linear parameter varying model based on a special structure deep neural network (DNN) is proposed to establish the predictive model to ensure prediction accuracy and modeling efficiency. Compared with common neural networks, an extra multiplying layer is inserted between the last hidden layer and the output layer which gives the output description of the DNN the ability to be transformed into the state space equations. Then the local optimization of the ACS can be constructed as a quadratic constraint problem with the state space predictive model. The optimizations are carried out at different isotherms within the flight envelope and an isotherm-based ACS is achieved which can be applied to the full-flight envelope by linear interpolation. Simulation results demonstrate that not only the proposed novel predictive model can achieve a high prediction accuracy, but also the ACS can effectively protect the engine from overlimit during acceleration at both design and off-design points. Thus, the effectiveness of the proposed method is validated.