In this work, we experimentally study the optical kerr nonlinearities of graphene/Si hybrid waveguides with enhanced self-phase modulation. In the case of CMOS compatible materials for nonlinear optical signal processing, Si and silicon nitride waveguides have been extensively investigated over the past decade. However, Si waveguides exhibit strong two-photon absorption (TPA) at telecommunication wavelengths, which lead to a significant reduction of nonlinear figure of merit. In contrast, silicon nitride based material system usually suppress the TPA, but simultaneously leads to the reduction of the Kerr nonlinearity by two orders of magnitude. Here, we introduce a graphene/Si hybrid waveguide, which remain the optical properties and CMOS compatibility of Si waveguides, while enhance the Kerr nonlinearity by transferring patterned graphene over the top of the waveguides. The graphene/Si waveguides are measured with a nonlinear parameter of 510 W-1m-1. Enhanced nonlinear figure-of-merit (FOM) of 2.48 has been achieved, which is three times higher than that of the Si waveguide. This work reveals the potential application of graphene/Si hybrid photonic waveguides with high Kerr nonlinearity and FOM for nonlinear all-optical signal processing.