Suspension system is one of the most effective vehicle components that play an essential role in the stability and comfort of the vehicle. The passive suspension can not fully meet a car's stability and comfort requirements. Instead, an active suspension system has been proposed to improve these challenges. Active suspension minimizes the vibrations entering the body using a closed-loop control system. To this end, in this research, an integral terminal sliding mode control (integral TSMC) for an active nonlinear car suspension system under external disturbances and uncertainties is designed. First, the integral TSMC is designed to deal with the uncertainties and the external disturbances in the system when the upper bound is known. Next, an adaptation law is recommended to estimate the upper bound of uncertainties and external disturbances. The results show that the proposed integral TSMC improves the convergence rate and tracking error of the closed-loop system. The stability of the nonlinear control system is investigated and proven using Lyapunov's stability theory. The numerical results indicate a good robust performance and stability for the proposed controller for the nonlinear suspension system with different road profiles in the presence of uncertainties and external disturbances. From the results, it can also be understood that important measures such as ride comfort, road holding, and mechanical structural limitations are met using the proposed approach.