I. INTRODUCTION The nuclear mass is of great importance not only for various aspects of nuclear physics, but also for weak-interaction studies and astrophysics [1]. In nuclear physics, it is helpful to study the nuclear symmetry energy and the synthesis of super-heavy nuclei by considering the more than 2000 measured nuclear masses. Theoretically, the mass of an atomic nucleus can be calculated by the macroscopic-microscopic method (such as the finite-range droplet model [2]) or the microscopic approaches (such as the Hartree-Fock Bogoliubov approach [3, 4]) or some other mass formulas [5]. The best mass formulas at present can reach about 0.6 MeV in the rms deviation for the usual data set of 2149 measured masses of nuclei (N and Z ≥ 8) [6] with about 24 ∼ 30 model parameters. Compared with the microscopic Hartree-Fock (HF) approaches, the macro-micro model is much faster in the calculation of the nuclear masses for the whole nuclear chart which provides a possibility for performing a large scale nuclear mass calculations to refine the model parameters and to explore the global behavior of nuclei. However, there are two crucial points in the macro-micro method should be further studied. The first one is that the consistency of the model parameters between the macroscopic and microscopic parts in the macro-micro method should be improved. It is known that although the finite-range droplet model (FRDM) is widely used in the calculations of nuclear mass, the parameter values in the calculation of the microscopic shell corrections are different from the corresponding values used in the macroscopic part of the model [1]. This less consistency between the macroscopic and microscopic parts may considerably reduce the credibility of extrapolations of the macroscopic-microscopic approach. On the other hand, with the great development of the experimental facilities for the study on super-heavy nuclei and nuclei far from the β -stability line, the influence of isospin effects on the nuclear mass formula attracted a great attention and should be given a better consideration. Based on above discussions an improved nuclear mass formula of self-consistently considering the isospin effects in both macroscopic and microscopic parts would be necessary to be established for providing a large scale nuclear mass calculations. To investigate the consistency of the model parameters between the macroscopic and microscopic parts in the macroscopic-microscopic approach and isospin dependence of the model parameters, the Skyrme energy density functional approach together with the ex- tended Thomas-Fermi (ETF) approximation [7, 8] is used. It is known that the energy 2