A new model-free adaptive digital integral-terminal-sliding-mode control algorithm is proposed for a class of nonlinear discrete-time systems with disturbances. The algorithm uses the discrete integral terminal sliding mode control algorithm to design the model-free adaptive controller based on the compact-format dynamic linearization model. Based on the technique of perturbation estimation to estimate the disturbance term of the system, and pseudo-partial derivatives(PPD) are estimated on-line from the I/O data of the system. The input and output bounded of the system is proved by theoretical analysis, and the validity of the proposed algorithm is verified by simulation experiment.