Grand canonical Monte Carlo (GCMC) simulations of ionic solutions with explicit solvent models are known to be challenging. One challenge arises from the treatment of long-range electrostatics and finite-box size in Monte Carlo simulations when periodic boundary condition and Ewald summation methods are used. Another challenge is that constant excess chemical potential GCMC simulations for charged solutes suffer from inadequate insertion and deletion acceptance ratios. In this work, we address those problems by implementing an oscillating excess chemical potential GCMC algorithm with smooth particle mesh Ewald and finite-box-size corrections to treat the long-range electrostatics. The developed GCMC simulation program was combined with GROMACS to perform GCMC/MD simulations of ionic solutions individually containing Li+, Na+, K+, Rb+, Cs+, F-, Cl-, Br-, I-, Ca2+, and Mg2+, respectively. Our simulation results show that the combined GCMC/MD approach can approximate the ionic hydration free energies with proper treatment of long-range electrostatics. Our developed simulation approach can open up new avenues for simulating complex chemical and biomolecular systems and for drug discovery.