Currently, the multijunction solar cell structure gives the highest efficiency for photovoltaic solar cells. In this study, tandem, triple, and quadruple junction multijunction solar cell structures that include an InP subcell on InP substrate were investigated. A model that can calculate both the voltage-current characteristics and external quantum efficiency was demonstrated. The model gave fitted results with the experimental data for a single junction GaAs solar cell and a tandem solar cell that provides efficiency higher than 30%. The model was used to optimize the lattice-matched AlAsSb/InP tandem, AlAsSb/InP/InGaAsP triple, and AlAsSb/InP/InGaAsP/GaAsSb quadruple junction solar cell designs and the highest efficiencies obtained for these cells were 29.9%, 36.69%, and 42.79%, respectively, under AM1.5 spectrum without any sun concentration. This lattice-matched quadruple junction structure gives the opportunity of having high efficiency without wafer bonding.