We propose an on-chip mode converter via two cascaded Bragg reflection processes. A forward conversion between two guided modes can be achieved with the aid of an additional mode. The proposed structure is theoretically studied and simulated via the rigorous three-dimensional finite-difference time-domain (3D-FDTD) method. The bandwidth and central wavelength of the proposed mode converter can be adjusted according to our theoretical analysis and simulation results. By applying the similar design approaches as fiber Bragg gratings, conversion spectra with different shapes can be obtained. As an example, several mode converters with bandpass and sidelobe-reduced spectra are designed. We also investigate and verify the mode conversion by experiment. Therefore, the proposed method may pave a new path for the mode converters with desired conversion spectra.