In this paper, a novel data-driven model-free adaptive predictive control method based on lazy learning technique is proposed for a class of discrete-time single-input and single-output nonlinear systems. The feature of the proposed approach is that the controller is designed only using the input-output (I/O) measurement data of the system by means of a novel dynamic linearization technique with a new concept termed pseudogradient (PG). Moreover, the predictive function is implemented in the controller using a lazy-learning (LL)-based PG predictive algorithm, such that the controller not only shows good robustness but also can realize the effect of model-free adaptive prediction for the sudden change of the desired signal. Further, since the LL technique has the characteristic of database queries, both the online and offline I/O measurement data are fully and simultaneously utilized to real-time adjust the controller parameters during the control process. Moreover, the stability of the proposed method is guaranteed by rigorous mathematical analysis. Meanwhile, the numerical simulations and the laboratory experiments implemented on a practical three-tank water level control system both verify the effectiveness of the proposed approach.