In a recent work, we developed a method [H. Takahashi et al., J. Chem. Phys. 143, 084104 (2015)] referred to as exchange-core function (ECF) approach, to compute exchange repulsion Eex between solute and solvent in the framework of the quantum mechanical (QM)/molecular mechanical (MM) method. The ECF, represented with a Slater function, plays an essential role in determining Eex on the basis of the overlap model. In the work of Takahashi et al. [J. Chem. Phys. 143, 084104 (2015)], it was demonstrated that our approach is successful in computing the hydrogen bond energies of minimal QM/MM systems including a cationic QM solute. We provide in this paper the extension of the ECF approach to the free energy calculation in condensed phase QM/MM systems by combining the ECF and the QM/MM-ER approach [H. Takahashi et al., J. Chem. Phys. 121, 3989 (2004)]. By virtue of the theory of solutions in energy representation, the free energy contribution δμex from the exchange repulsion was naturally formulated. We found that the ECF approach in combination with QM/MM-ER gives a substantial improvement on the calculation of the hydration free energy of a hydronium ion. This can be attributed to the fact that the ECF reasonably realizes the contraction of the electron density of the cation due to the deficit of an electron.