A lattice matched triple junction solar cell (TJSC) structure with a GaAs0.58 P0.42 top cell and bandgap tunable GaNxAs1-x-zPz middle and bottom cells on virtual SiGe substrate is proposed in this study. SiGe/Si substrate is preferred as it is a low-cost substrate and because it provides a lattice constant at which bandgap tunable dilute nitride materials that are appropriate for highly efficient multijunction solar cells can be obtained. By changing the nitrogen content in GaNxAs1-x-zPz, the bandgap of the middle and bottom subcells is adjusted to the optimum values. The bandgap of the top cell is constant at 1.95 eV. Three models with different values of surface recombination velocities and Shockley–Read–Hall recombination lifetimes are applied to the presented TJSC structure. Peak efficiencies of 48.9%, 40.6% and 33.7% are achieved at EG2 = 1.45 eV and EG3 = 1.04 eV for Model 1, EG2 = 1.45 eV and EG3 = 1.15 eV for Model 2, and EG2 = 1.5 eV and EG3 = 1.17 eV for Model 3, respectively. A fourth bandgap adjustable GaNxAs1-x-zPz junction is inserted into the system and a significant improvement is obtained under high sun concentration for Models 1 and 2. The presented original results are very promising because the variable bandgaps provide very efficient absorption of incoming spectrum.