We report a 2-µm all-fiber nonlinear pulse compressor based on a tapered Pb-silicate photonic crystal fiber (PCF), which is capable of achieving large compression with low pedestal energy. A tapered Pb-silicate photonic crystal fiber with increased nonlinear coefficients is proposed for achieving self-similar pulse compression (SSPC) at 2 µm. The dynamic evolution of the fundamental order soliton is numerically analyzed based on the designed tapered fiber. After pulse compression in a tapered fiber with a length of 2.2 m, an initial 1.76 ps pulse can be compressed to 88 fs, increasing the peak power from 4.4 to 86 W with a compression factor of 20 and a quality factor of 98%. The results reveal that exponential variation yields superior compression performance and provides a promising solution for generating high-power femtosecond pulses at 2 µm.