Due to their compactness, neutron stars are the best study matter in high density and strong-field gravity. Hartle and Thorne have proposed a good approximation or perturbation procedure within general relativity for slowly rotating relativistic stars by assuming the matter inside the stars is an ideal isotropic fluid. This study extends the analytical Hartle–Thorne formalism for slowly rotating neutron stars, including the possibility that the neutron star pressure can be anisotropic. We study the impact of neutron stars’ anisotropy pressure on mass correction and deformation numerically. For the anisotropic model, we use the Bowers-Liang model. For the equation of state of neutron stars, we use a relativistic mean-field BSP parameter set with the hyperons, and for the crust equation of state, we use the one of Miyatsu et al. We have found that the mass of neutron stars increases but the radius decreases by increasing λBL value. Therefore, the NS compactness increases when λBL becomes larger. This fact leads to a condition in which NS is getting harder to deformed when the λBL increased.