We demonstrate the two-color cooling and trapping of alkaline-earth atoms in a grating magneto-optical trap (GMOT). The trap is formed by a single incident laser beam together with four secondary beams that are generated via diffraction from a nanostructured wafer. A grating structure for a GMOT operating with strontium atoms is optimized and fabricated. We trap 10688Sr atoms on the 1S0→1P1 transition at 461nm and transfer 25% of these atoms to the second cooling stage on the narrower 1S0→3P1 intercombination transition at 689nm, preparing a sample of 2.5×105 atoms at 5μK. These results demonstrate the applicability of the GMOT technology in conjunction with two widely differing wavelengths and enable the continued miniaturization of alkaline-earth-based quantum technologies like optical atomic clocks.