The high-order perturbative density functional theory (DFT) for a nonuniform hard-sphere fluid (S. Zhou and E. Ruckenstein, Phys. Rev. E, 61, 2704, (2000)) was truncated at the third order and reformulated to be adapted for nonuniform non-hard-sphere interaction potential fluids. The only required input parameter (the second-order direct correlation function of a uniform fluid) can be obtained from the Ornstein-Zernike equation numerically or analytically. The constant relating to the bulk fluid parameter and measuring the strength of the third-order term was determined by the sum rule, which specifies the bulk pressure by the hard-wall contact density. The present third-order perturbative DFT predicted density distribution profiles for a Lennard-Jones fluid and an adhesive hard-sphere fluid confined between two hard walls that are in very good agreement with the simulation data. Furthermore, the present third-order perturbative DFT predicted very well the contact density as a function of the gap width for the confined adhesive hard-sphere fluid.