Abstract: In this paper, using the Skyrme energy density functional theory, we have investigated the effect of different treatment of pairing correlations, e.g., Hartree-Fock-Bogoliubov (HFB), Hartree-Fock-Bogoliubov Lipkin-Nogami (HFBLN), and particle number projection on HFBLN, etc., on the potential energy surface (PES) calculations and ground-state energy. We also tested the effect of different pairing force, such as volume-pairing, surface-pairing, mixed-pairing force. We studied typical doubly-magic nuclei, such as ¹⁶O, ⁴⁰Ca, ¹⁰⁰Sn and ²⁰⁸Pb, which have spherical shape in their ground states. We studied the typical deformed nucleus ⁴⁸Cr, and the binding energies of Cr and Fe isotopes. The PES of superheavy nucleus ²⁹⁸Fl is also studied. It is learned that the deformed minimum is not changed much by different pairing correlations. The pairing correlations bring about several MeV to the total binding energies. The correlation energy brought by HFBLN is more than that by HFB approximation, and that by projection method increases further. The softness of the deformed minimum is also changed by pairing correlations. The one by HFBLN is softer than the one by HFB. However, the deformed minimum become explicit by projection method. Pairing correlation can lower down the barrier in the PES. In the same approximation of the pairing correlation, PES results calculated by mixed-pairing and volume-pairing force are similar. It seems that in the PES calculations, the surface pairing force can bring more pairing correlations, thus the effect of surface pairing force is larger than that of volume- and mixed-pairing forces.