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We propose and simulate the mid-infrared (MIR) frequency comb generation based on the Kerr nonlinear effect in a silicon microring resonator (MRR). The MRR is formed by the suspended ridge waveguides which are designed to have the anomalous group-velocity dispersion. Taking the thermal effect into consideration, the modified Lugiato–Lefever equation (LLE) is used to simulate the frequency comb generation. The stable dissipative cavity soliton and mode-locked combs in the MIR wavelength range of 2.5 μm–5.2 μm can be obtained under different pump conditions. It is found that the ternary-pump scheme has wider bandwidth and flatter frequency combs as compared with the dual-pump scheme. The lowest total pump power is required for the ternary-pump approach to produce the same comb span in these three pump conditions. Keywords: Kerr frequency combs, Microring resonator, Mid-infrared, Ternary-pump, Silicon photonics