with isospin asymmetry I = ( N − Z ) /A . The pairing term proposed in [11] is adopted, with In this work, the symmetry energy coefficient of finite nuclei is written as, based on the conventional surface-symmetry term [12, 13] of liquid drop model, with a small correction term for description of isospin dependence of a$_{sym}$ . The sensitive dependence of symmetry energy coefficient on the asymmetry of nucleus, especially that a$_{sym}$ increases with increasing proton fraction of the system is also found in [14]. The introduced I correction term approximately describes the Wigner effect [2] of heavy nuclei. For a heavy nucleus near the β -stability line ( A | I | ≫ 2 ≫ | I | ), the introduced I term in a$_{sym}$ roughly leads to a correction ∝ | I | (known as Wigner term) to the binding energy of the nucleus. Compared with the case without the I term being taken into account, the rms deviation of nuclear masses defined as σ 2 = 1 m ∑ ( M ( i ) exp − M ( i ) th ) 2 from the measured masses AME2003 [6] for the 2149 nuclei ( N and Z ≥ 8) is reduced by about 6%. Furthermore, we find when the isospin dependence of symmetry energy coefficient is taken into account, the obtained optimal c$_{sym}$ increases about 3 MeV and up to 29 MeV which is close to the symmetry energy coefficient of nuclear matter at saturation density obtained from the Skyrme energy density functional. The Coulomb exchange correction and surface diffuseness correction to the Coulomb energy is approximately taken into account as the term Z − 2 / $^{3}$. In addition, the terms b$_{k}$ in Eq.(1) which are obtained according to the Skyrme energy density functional (the detailed discussion is in the next subsection) describe the contribution of nuclear deformation to the macroscopic energy. 4 a$_{sym}$ = c$_{sym}$ [ 1 − κ A 1 / 3 + 2 − | I | 2 + | I | A ] , (4) δ$_{np}$ =        2 − | I | : N and Z even | I | : N and Z odd 1 − | I | : N even , Z odd , and N > Z 1 − | I | : N odd , Z even , and N < Z 1 : N even , Z odd , and N < Z 1 : N odd , Z even , and N > Z (3)