The fabrication of a low reabsorption emission loss, high efficient luminescent solar concentrator (LSC) is demonstrated by embedding near infrared (NIR) core/shell quantum dots (QDs) in a polymer matrix. An engineered Stokes shift in NIR core/shell PbS/CdS QDs is achieved via a cation exchange approach by varying the core size and shell thickness through the refined reaction parameters such as reaction time, temperature, precursor molar ratio, etc. The as-synthesized core/shell QDs with high quantum yield (QY) and excellent chemical/photostability exhibit a large Stokes shift with respect to the bare PbS QDs due to the strong core-to-shell electrons leakage. The large-area planar LSC based on core/shell QDs exhibits the highest value (6.1% with a geometric factor of 10) for optical efficiency compared to the bare NIR QD-based LSCs and other reported NIR QD-based LSCs. The suppression of emission loss and the broad absorption of PbS/CdS QDs offer a promising pathway to integrate LSCs and photovoltaic devices with good spectral matching, indicating that the proposed core/shell QDs are strong candidates for fabricating high efficiency semi-transparent large-area LSCs.