We present design, fabrication, and characterization of a silicon-on-insulator grating coupler of high efficiency for coupling between a silicon nanophotonic waveguide and a single mode fiber. By utilizing the lag effect of the dry etching process, a grating coupler consisting of nonuniform grooves with different widths and depths is designed and fabricated to maximize the overlapping between the upward wave and the fiber mode. The measured waveguide-to-fiber coupling efficiency of 64% (-1.9 dB) for the transverse electric polarization is achieved by the present nonuniform grating coupler directly defined on a regular silicon-on-insulator wafer.