for the whole nuclear chart is much shorter than that with the microscopic mass formula models. At the same time the consistency of the model parameters between the macroscopic and microscopic parts greatly promotes the credibility of extrapolations in the macroscopic- microscopic approach. In order to extend the mass formula to super-heavy nuclei and the nuclei far from the β -stability line, we pay a special attention to study the isospin and mass dependence of the model parameters including symmetry energy coefficient and the symmetry potential, etc. Those studies are based on the Skyrme energy density functional approach together with the extended Thomas-Fermi approximation. Since more sufficiently considering the isospin effects of the model parameters the formula could systematically study super-heavy nuclei and the nuclei far from the β -stability line. To further test the model, the appearance of new magic number N = 16 in light neutron- rich nuclei and the shape coexistence phenomena for some nuclei have been examined with the model. Our results are in good agreement with some experimental and theoretical studies. The predicted super-heavy island according to the obtained shell corrections of nuclei looks flat. Along nuclei with Z = 114 or N = 178, we find a relatively deeper valley in the contour plot of shell corrections. The shell corrections of nuclei around $^{292}$114 are about − 6 MeV and much smaller (in absolute value) than the corresponding results from the finite-range droplet model. The calculated nuclear masses for highly neutron-rich heavy nuclei from the three different models have large deviations. The results of our model are relatively close to those of HFB-17 for most nuclei. We thank Prof. W. Scheid for a careful reading of the manuscript. We also thank Prof. Zhuxia Li and an anonymous referee for valuable suggestions. This work was supported by National Natural Science Foundation of China, Nos 10875031, 10847004 and 10865002. The obtained mass tables with the proposed formula are available from http://www.imqmd.com/wangning/publication.html ACKNOWLEDGEMENTS [1] D. Lunney, J.M. Pearson, C. Thibault, Rev. Mod. Phys. 75 (2003) 1021. [2] P. M¨ oller, J. R. Nix, et al., At. Data and Nucl. Data Tables 59 (1995) 185. 18