The traditional lattice matched GaInP/(In) GaAs/Ge triple-junction (3J) solar cell has no much room to enhance its practical achievable conversion efficiency because of its inappropriate ensemble of bandgap energies. According to the P-N junction formation mechanism and the close equilibrium condition, we explore a series of computational codes in the framework of MATLAB to simulate and optimize the inverted structure of series-connected 3J solar cells with a fixed top bandgap of 1.90 eV on GaAs substrate. In this paper, structural optimization is conducted in the real device design, because the realistic (QE) is closely related to a set of material parameters in the subcell, i.e., the absorbtion coefficient of material, subcell thickness, minority carrier diffusion length, surface recombination velocity, etc. The results indicate improved inverted 3J solar cells with nearly optimized bandgaps of 1.90, 1.38, and 0.94 eV, by utilizing two independently lattice-mismatches (0.17% and 2.36% misfit respectively) to the GaAs substrate. A theoretical efficiency of 51.25% at 500 suns is demonstrated with this inverted design with the optimal thickness (4 m GaInP top and 3.1 m InGaAs middle). By contrast, the efficiency with the infinite thickness of subcells is reduced by 1%, which is mainly attributed to the effect of minority carrier recombination on Jsc. Exactly speaking, if photo-generated carriers make a contribution to Jsc, they must be collected effectively by the P-N junction before recombining. A new model is proposed based on the effect of dislocation on the metamorphic structure properties by regarding dislocation as minority-carrier recombination center. Our calculation indicates that threading dislocations density in the middle junction is approximate to 1.70105 cm-2 when dislocations in the gradient buffer layer are neglected. The theoretical efficiency is increased by 0.3% compared with the inverted design containing a single metamorphic junction. As a result, based on the two metamorphic combinations, a solar cell with an area of 30.25 mm2 is prepared. The efficiency of the designed cell with two lattice-mismatched junctions reaches 40.01% at 500 suns (AM1.5D, 38.4 W/cm2, 25℃), which is 0.4% higher than that of the single metamorphic junction 3J solar cell.