Lasers with high average and high peak power as well as ultrashort pulse width have been all along demanded by nonlinear optics studies, strong-field experiments, electron dynamics investigations, and ultrafast spectroscopy. While the routinely used titanium-doped sapphire (Ti:sapphire) laser faces a bottleneck in the average power upscaling, ytterbium (Yb)-doped lasers have remarkable advantages in achieving high average power. However, there is still a substantial gap of pulse width and peak power between the Ti:sapphire and Yb-doped lasers. Here we demonstrate a high-power $\mathrm{Yb}\text{:}{\mathrm{CaAlGdO}}_4$ (Yb:CALGO) regenerative amplifier system, delivering 1040 nm pulses with 11 W average power, 50 fs pulse width, and 3.7 GW peak power at a repetition rate of 43 kHz, which to some extent bridges the gap between the Ti:sapphire and Yb lasers. An ultrabroadband Yb-doped fiber oscillator, specially designed spectral shapers, and Yb:CALGO gain medium with broad emission bandwidth, together with a double-end pumping scheme enable an amplified bandwidth of 19 nm and 95 fs output pulse width. To the best of our knowledge, this is the first demonstration of sub-100 fs regenerative amplifier based on Yb-doped bulk medium without nonlinear spectral broadening. The amplified pulse is further compressed to 50 fs via cascaded-quadratic compression with a simple setup, producing 3.7 GW peak power, which boosts the record of peak power from Yb:CALGO regenerative amplifiers by 1 order. As a proof of concept, pumped by the high-power, 50 fs pulses, 7.5–11.5 µm mid-infrared (MIR) generation via intrapulse difference-frequency generation is performed, without the necessity of nonlinear fiber compressors. It leads to a simple and robust apparatus, and it would find good usefulness in MIR spectroscopic applications.