In this paper, a novel silicon-on-insulator (SOI) waveguide with the multiperiod vertical grating is proposed to realize broadband parametric wavelength conversion with a quasi-phase matching technique. The grating period in the former part of the SOI waveguide is optimized to enhance the conversion efficiency at designated signal wavelength and the 3-dB bandwidth. When the continuous-wave pump at 1550 nm is used, the conversion efficiency of -14.0 dB at 1750 nm and the 3-dB bandwidth of 387 nm can be obtained. Compared to the constant-width waveguide, the improvements of 26.7 dB and 298 nm are achieved, respectively. The results show that this SOI waveguide is an ideal device for broadband wavelength conversion without dispersion engineering.