We study dielectric diffraction gratings for light-trapping in quantum well solar cells and compare their performance with plasmonic and Lambertian light-trapping structures. The optimum structural parameters are identified for symmetric uni-periodic, symmetric bi-periodic and asymmetric bi-periodic gratings. The enhancement in short-circuit current density from the quantum well region with respect to a reference cell with no diffraction grating is calculated. The ratio of this enhancement to the maximum achievable enhancement (i.e. no transmission losses) is 33%, 75% and 74%, respectively for these structures. The optimum asymmetric and symmetric bi-periodic structures perform closest to Lambertian light-trapping, while all three optimum grating structures outperform optimum plasmonic light-trapping. We show that the short-circuit current density from the quantum well region is further enhanced by incorporating a rear reflector. © 2013 Optical Society of America.