We report optical parametric amplification (OPA) of low-frequency infrared pulses in the intermediate region between terahertz (THz) frequency and mid-infrared (MIR), i.e., from 16.9 to 44.8 THz. The 255-fs laser output of the Yb:KGW regenerative amplifier is compressed to 11-fs pulses using a multi-plate broadening scheme, which generates THz-to-MIR pulses with a spectrum extending to approximately 50 THz by intra-p1ulse differential frequency generation (DFG) in GaSe. The THz-to-MIR pulses are further amplified using a two-stage OPA in GaSe. The temporal dynamics and photocarrier effects during OPA are characterized in the time domain. Owing to the intra-pulse DFG, the long-term phase drift of the THz-to-MIR pulses after two-stage OPA is as small as 16 mrad during a 6-h operation without any active feedback. Our scheme using the intra-pulse DFG and post-amplification proposes a new route to intense THz-to-MIR light sources with extreme phase stability.