Frequency-modulated (FM) laser combs, which offer a quasi-continuous-wave output and a flat-topped optical spectrum, are emerging as a promising solution for wavelength-division multiplexing applications, precision metrology, and ultrafast optical ranging. The generation of FM combs relies on spatial hole burning, group velocity dispersion, Kerr nonlinearity, and four-wave mixing (FWM). While FM combs have been widely observed in quantum cascade Fabry-Perot (FP) lasers, the requirement for a low-dispersion FP cavity can be a challenge in platforms where the waveguide dispersion is mainly determined by the material. Here we report a 60 GHz quantum-dot (QD) mode-locked laser in which both the amplitude-modulated (AM) and the FM comb can be generated independently. The high FWM efficiency of –5 dB allows the QD laser to generate FM comb efficiently. We also demonstrate that the Kerr nonlinearity can be practically engineered to improve the FM comb bandwidth without the need for GVD engineering. The maximum 3-dB bandwidth that our QD platform can deliver is as large as 2.2 THz. This study gives novel insights into the improvement of FM combs and paves the way for small-footprint, electrically pumped, and energy-efficient frequency combs for silicon photonic integrated circuits (PICs).