Grating couplers are developed as one of the building blocks in silicon photonics to couple light between on-chip devices and optical fibers. For emerging high-capacity datacom and telecom systems enabled by space division multiplexing, it is essential to couple light together with mode conversion functions. In this work, we show the feasibility of combining conventional grating couplers and mode converters, both with a high efficiency. The proposed devices are very compact, built on standard silicon-on-insulator wafers, with no extra fabrication efforts required. It is shown that the LP01, LP11a, LP11b, and LP21b modes in a few-mode optical fiber can be successfully excited directly from the proposed grating couplers, which have the fundamental mode as an input from an integrated waveguide. The overall coupling efficiency, including mode conversion efficiency, can be as high as 50%. We also analyze the performance of the grating couplers in terms of bandwidth, efficiency, and tolerance to device fabrication errors.