Maximizing the conversion of sunlight to electricity by theoretically optimizing the utilization of lattice-matched multi-junction photovoltaic cells of the incident solar radiation was attempted. The lattice constant matching among the layers is important to avoid the internal thermal stress. In the proposed model the current mismatching, the thermalization losses, and the fill factor were all introduced to the conversion efficiency equation. The current matching can be achieved not only by suitable choice of bandgap energies, which directly decides the photon count distribution among the junctions, but also, by the absorbed amounts of those photons that could be controlled effectively by optimal choice of thicknesses; which is the significance of this research since such additional design freedom is essential to overcome the possible imperfect choice of bandgap energies that is dictated by the lattice matching requirement. Numerical search method was employed to fmd the optimal thicknesses for two- and three-junction PV solar cells in order to maximize the conversion efficiency. The performance of the proposed model is tested for various lattice-matched MJ samples. The results revealed that employing well-chosen bandgap energies for the active media in these samples leads to promising and efficient electricity generation using MJ solar cells. For example, 41.6% and 46.7% solar to electricity conversion efficiency can be obtained from double and triple junction solar cells, respectively, under concentrated sun regime.