We present a hybrid graphene-silicon waveguide, which consists of a lateral slot waveguide with three layers of graphene flakes inside. Through a theoretical analysis, an effective index variation for about 0.05 is found in the waveguide by applying a voltage on the graphene. We designed a Mach-Zehnder modulator based on this waveguide and demonstrated it can process signals nearly chirp-free. The calculation shows that the driving voltage is only 1 V even if the length of the arm is shortened to be 43.54 μm. An extinction up to 34.7 dB and a minimum chirp parameter of -0.006 are obtained. Its insertion loss is roughly -1.37 dB. This modulator consumes low power and has a small footprint. It can potentially be ultrafast as well as CMOS compatible.