density functional theory is widely used in the study of the nuclear ground state which provides us with a useful balance between accuracy and computation cost allowing large systems with a simple self-consistent manner. With the Skyrme energy density functional approach, we systematically investigate some ground state properties of nuclei, such as the nuclear symmetry energy coefficient, the deformation energy and the symmetry potential, which are helpful to improve the macro-micro method. Based on these calculations, we propose a semi-empirical nuclear mass formula by taking into account the isospin and mass dependent model parameters. The paper is organized as follows: In Sec. II, the proposed mass formula is introduced. In Sec. III, some calculation results are presented. Finally, a summary is given in Sec. IV. In this section, we first introduce the macroscopic part of the mass formula. Then, the influence of nuclear deformation on the macroscopic energy of nucleus are investigated with the Skyrme energy density functional approach and the single particle potential used in the calculation of the microscopic shell correction is introduced. In addition, the symmetry potential and the symmetry energy coefficient of nuclear matter is also investigated. Finally, the parameters adopted in the model are presented. We start with the macroscopic-microscopic method [2, 9]. The total energy of a nucleus can be calculated as a sum of the liquid-drop energy and the Strutinsky shell correction Δ E , The liquid drop energy of a spherical nucleus E$_{LD}$ ( A, Z ) is described by a modified Bethe- Weizs¨ acker mass formula [10], 3 E$_{LD}$ ( A, Z ) = a$_{v}$A + a$_{s}$A 2 / 3 + a$_{c}$ Z ( Z − 1) A 1 / 3 ( 1 − Z − 2 / $^{3}$) + a$_{sym}$I $^{2}$A + a$_{pair}$A − 1 / $^{3}$δ$_{np}$ (2) E ( A, Z, β ) = E$_{LD}$ ( A, Z ) ∏ k ≥ 2 ( 1 + b$_{k}$β 2 k ) + Δ E ( A, Z, β ) . (1) II. THE MODEL A. Modified Bethe-Weizs¨acker Mass Formula