A mid-infrared (mid-IR) optical parametric chirped pulse amplification (OPCPA) system generating few-cycle pulses with multi-gigawatt peak power at a 1 kHz repetition rate is reported. The system is pumped by a highly stable 2 μm picosecond chirped pulse amplifier based on Ho:YLF gain media to exploit the high nonlinearity of ZnGeP2 (ZGP) crystals for parametric amplification. The ZGP optical parametric amplification (OPA) is characterized by a high conversion efficiency of >10 %, resulting in 1.3 mJ idler pulses at a center wavelength of 5.1 μm. Employing a dispersion management scheme based only on bulk materials, pulses as short as 160 fs are obtained. By adding a spatial light modulator in the OPCPA setup, the pulses are further recompressed to 75 fs duration which corresponds to less than five optical cycles. Taking into account the pulse energy of 0.65 mJ in this configuration, it translates into a peak power of 7.7 GW. The achieved pulse durations and peak powers, to the best of our knowledge, represent record values for high-energy mid-IR OPCPAs beyond 4 μm.