We demonstrate a Yb:CaGdAlO4 (Yb:CALGO) bulk regenerative amplifier (RA) capable of delivering a peak power of 0.112 TW at a 1 kHz repetition rate. By integrating a home-built ultrabroadband nonlinear polarization evolution (NPE) mode-locked fiber oscillator, a set of custom-designed spectral shapers and the broad emission bandwidth Yb:CALGO gain medium, an amplified bandwidth of 18.2 nm and an output pulse duration of 137 fs are achieved. Thanks to the thermally insensitive dual-crystal cavity design and the quasi-continuous pumping thermal management scheme, the RA achieves a maximum pulse energy output of 21.01 mJ. Under the constraint of avoiding crystal damage, the compressed pulse energy reaches 17.6 mJ. To the best of our knowledge, this represents the highest pulse energy and peak power ever achieved from a Yb:CALGO RA. The power stability over 30 minutes is measured to be 0.506%, and the beam quality factor M2 is 1.16 × 1.12.