This paper proposes an adaptive integral non-singular terminal sliding mode control in combination with a neural network (INTSMC-NN) for nonlinear servo-hydraulic actuator systems. The proposed controller has the advantages of the conventional non-singular terminal sliding mode control; it can tolerate external disturbances, evades the singularity problem of the conventional terminal sliding mode control, and also guarantees finite time convergence of states. The main problem and drawback of the sliding mode-based control is the chattering phenomenon which is caused by the switching part of the controller. This phenomenon can cause severe impacts on mechanical components of the hydraulic system. In order to overcome to this issue, and moderate the control signal, the discontinuous part of the controller is replaced by a neural network. The stability of the controller is investigated through Lyapunov stability criteria. To study the performance of the proposed INTSMC in combination with neural network a third-order nonlinear servo-hydraulic actuator is considered. Simulation results first, indicates the capability of the proposed method in eliminating the chattering from the control signal and also making the system states to track the desired trajectory with high accuracy. Second, the performance of the proposed integral NTSMC is studied and compared to the conventional NTSMC.