On the basis of a traditional hard sphere square well (HSSW) model, we first test the performance of a recently proposed thermodynamic perturbation theory (TPT) originating from a coupling parameter expansion. It is concluded that (1) the coupling parameter expansion-TPT predicts a second-order term of the perturbation expansion far more accurately than several previous approximations including a well-known macroscopic compressibility approximation; (2) the fifth-order TPT is generally a little more accurate than the third-order TPT. Next, global phase diagrams of the HSSW model with several representative potential range parameter values are calculated by the fifth-order TPT for the fluid phase combined with a first-order TPT for the solid phase, and found in satisfactory agreement with those as found from available computer simulation. Once more, we theoretically compute the fluid phase critical curve, solid phase isostructural critical curve, and triple curve as a function of the potential range parameter of the HSSW model and an additional hard core attractive Yukawa (HCAY) model, respectively. It is found that these phase lines of the HSSW model gauging the outlines of phase diagrams display abnormity compared with those of the HCAY model; particularly a huge abnormity of the HSSW case is always related to participation of the solid phase. We explain that the abnormity originates from a combination of a discontinuity of the SW tail and a highly discrete situation of the particles in the solid phase. The present investigation eliminates the possibility of the HSSW potential as a feasible model of real fluids; the opportunity of the HSSW is perhaps narrowed as sample potential for testing theories harshly.