In this letter, it is pointed out that an ideal universal equation of state (EOS) of solids should have four merits. The EOS corresponding to the generalized Lennard-Jones (GLJ) potential is derived. It is pointed out that the GLJ EOS is not volume analytic, as the exponents contained in the potential function take arbitrary values. On making the exponents satisfy a relationship, the GLJ EOS becomes volume analytic with two parameters (mGLJ EOS), and has all four merits. By applying six EOSs in investigating 50 materials, it is shown that the mGLJ EOS gives the best results.