Self-similar pulse compression has important application in highly coherent supercontinuum (SC) generation. In this paper, we numerically present the mid-infrared self-similar picosecond pulse compression in a tapered suspended silicon strip waveguide, which is designed with exponentially decreasing dispersion profile along the direction of propagation. When the variation of the Kerr nonlinear coefficient γ(z), linear and nonlinear losses, higher-order nonlinearity, and higher-order dispersion are taken into consideration, the simulation result shows that a 1 ps input pulse centered at wavelength 2.8μm could be self-similarly compressed to 47.06 fs in a 3.9-cm waveguide taper, along with a compression factor Fc of 21.25, quality factor Qc of 0.78, and negligible pedestal. After that, the compressed pulse is launched into a uniform silicon strip waveguide, which is used for the generation of SC. We numerically demonstrate that the coherence of the generated SC by the compressed pulse can be significantly improved when compared to that generated directly by the picosecond pulse. The simulation results can be used to realize on-chip mid-infrared femtosecond light source and highly coherent supercontinuum, which can promote the development of on-chip nonlinear optics.