Luminescent solar concentrators are cost-effective complements to semiconductor photovoltaics that can boost the output of solar cells and allow for the integration of photovoltaic-active architectural elements into buildings (for example, photovoltaic windows). Colloidal quantum dots are attractive for use in luminescent solar concentrators, but their small Stokes shift results in reabsorption losses that hinder the realization of large-area devices. Here, we use ‘Stokes-shift-engineered’ CdSe/CdS quantum dots with giant shells (giant quantum dots) to realize luminescent solar concentrators without reabsorption losses for device dimensions up to tens of centimetres. Monte-Carlo simulations show a 100-fold increase in efficiency using giant quantum dots compared with core-only nanocrystals. We demonstrate the feasibility of this approach by using high-optical-quality quantum dot–polymethylmethacrylate nanocomposites fabricated using a modified industrial method that preserves the light-emitting properties of giant quantum dots upon incorporation into the polymer. Study of these luminescent solar concentrators yields optical efficiencies >10% and an effective concentration factor of 4.4. These results demonstrate the significant promise of Stokes-shift-engineered quantum dots for large-area luminescent solar concentrators.