The characteristics of ground state X2Πi and the first excited state A2Σ+ of HF+ under spin-orbit coupling are studied by using the multi-configuration quasi-degenerate perturbation theory. The vertical excited energy is v[2Π1/2 (v = 0)→ X2Π3/2(v = 0)] = 285.176 cm-1, and the potential energy curves of the splitting electronic states X2Π3/2, 2Π1/2 of X2Πi are obtained. The analytical potential functions of these states are derived by employing the Murrell- Sorbie function (M-S) and the least-square fitting method, and then the spectroscopic constants for X2Π3/2, 2Π1/2 and A2Σ+ are derived from the M-S function. All the spectroscopic data and the analytical potential functions for states X2Π3/2 and 2Π1/2 are given for the first time in our calculation.