The splitting of potential energy curves for the states X2∏3/2, 2∏1/2 and A2∑+ of hydroxyl OH under spin-orbit coupling (SOC) has been calculated by using the SO multi-configuration quasi-degenerate perturbation theory (SOMCQDPT). Their Murrell-Sorbie (M-S) potential functions have been derived, then, the spectroscopic constants for X2∏3/2,2∏1/2 and A2∑+ have been derived from the M-S function. The calculated dissociation energies for the three states are D0[OH(X2∏3/2)]=34966.632cm-1, D0[OH(2∏1/2)]=34922.802cm-1, and D0[OH(A2∑+)]=17469.794cm-1,respectively. The vertical excitation energy v[2∏1/2(v = 0) → X2∏3/2(v = 0)] = 139.6cm-1. All the spectroscopic data for the X2∏3/2 and 2∏1/2 are given for the first time except the dissociation energy of X2∏3/2.