An improved compact format model free adaptive control (iCF-MFAC) method based on an equivalent dynamic linearization technique is proposed for a class of discrete-time nonlinear systems described by a general nonlinear function. The adaptive control law of the iCF-MFAC method consists of two parts: A time-varying proportional control term and a time-varying integral control term. Compared with the corresponding original CF-MFAC method with only a time-varying integral term, the iCF-MFAC method is not only more universal and flexible, but also can provide a better dynamical control performance. In addition, the comparison is also made between the iCF-MFAC method and an MFAC method that has a similar controller structure and is based on a full format dynamic linearization data model. With the same controller parameters, the iCF-MFAC can yield a faster output response. Then, the convergence and stability of the resulting closed-loop iCF-MFAC system are proved through rigorous analysis. Both numerical simulations and practical experiments are carried out to demonstrate the effectiveness and feasibility of the proposed method.