To improve the the absorption of the incoming light spectrum in the cell, the bandgap modulation is performed in the cell. such a cell is designed here, with the help of quantum well region of InP material and GaInP barrier region. The bandgap engineered GaAsP solar cell having the bandgap of 1.48eV is utilized along with the InP quantum well material with bandgap energy of 1.35eV. The quantum well absorbs the lower bandgap photon energy, which improves the photo carriers. A type-A bandgap structure is formed in the quantum well region, which results in enhanced utilization of lower bandgap photon energy. The Analysis show the significant absorption of the incoming light spectrum, which reflects in the improvement of the current density. The trade-off between the short circuit current and open circuit voltage, which happens due to the bandgap modulation, leads to the 20% drop in the open circuit voltage. But, due to larger improvement of 31.06% in the short circuit current leads to the improvement of 4.75% in overall efficiency of the cell. The quantum efficiency of the cell is well above 90%. The bandgap modulated quantum well solar cell achieves 25.76% efficiency for the formation of the p-i-n region. AM1.5G environment under 1-Sun spectrum is used to illuminate the designed solar cell.