In this paper, we design a tapered tellurite photonic crystal fiber (TTPCF) with nonlinear coefficient increasing along the propagation direction, and demonstrate the mid-infrared self-similar pulse compression of the fundamental soliton in such a TTPCF. When the variation of group-velocity dispersion, higher-order dispersion, higher-order nonlinearity, and linear loss are considered, a 1 ps pulse at wavelength 2.5 μm can be compressed to 62.16 fs after a 1.63-m long propagation, along with the negligible pedestal, compression factor Fc of 16.09, and quality factor Qc of 83.16%. Then the compressed pulse is launched into another uniform tellurite PCF designed, and highly coherent and octave-spanning supercontinuum (SC) is generated. Compared to the initial picosecond pulse, the compressed pulse has much larger tolerance of noise level for the SC generation. Our research results provide a promising solution to realize the fiber-based mid-infrared femtosecond pulse source for nonlinear photonics and spectroscopy.