Attosecond science is one of the driving forces for developing the femtosecond amplifiers of high average power and ultrashort pulse duration. In this work, the regenerative amplification is studied experimentally and theoretically based on Yb:CaYAlO₄ crystal for the practical needs of high-repetition-rate attosecond light sources. In the theoretical study, a mode-tunable regenerative cavity with good thermal stability is designed based on the thermal lens calculations of Yb:CaYAlO₄ crystal; the amplified output energy and spectra of π and σ polarization of the crystal are calculated. In the experiment, the π-axis of Yb:CaYAlO₄ crystal is parallel to the laser polarization, and the laser amplifier emits 1.61 mJ pulses with average power 16.1 W. Notably, the dip of the π-polarization emission spectrum near 1025.1 nm compensates for the gain narrowing of the seed laser during amplification. Thus, the center wavelength and the spectral full width at a half maximum of the amplified laser are 1030 nm and 16 nm respectively. Using a grating-pair for compression, 149 fs pulses with peak power 9.5 GW are obtained. In comparison, the σ-polarization emission spectrum of Yb:CaYAlO₄ crystal is relatively flat in a range from 1000 to 1050 nm, but with a larger gain cross-section. When the laser polarization is parallel to the σ-axis of Yb:CaYAlO₄ crystal, 2.87 mJ pulses at 10 kHz repetition rate are achieved, with an average power of 28.7 W. In this case, the center wavelength and the spectral full width at half maximum of the amplified laser are 1037 nm and 11 nm respectively. Using a grating-pair for compression, 178 fs pulses with peak power of 14.2 GW are obtained. The beam quality factor measured is 1.09 along the x-axis of the amplified laser and 1.17 along the y-axis. To the best of our knowledge, this is the highest average power and the maximum pulse energy obtained from the Yb:CaYAlO₄ amplifier. For applications in high-repetition-rate attosecond light sources, terahertz generation and optical parametric amplification, subsequent laser outputs with average power 200 W, pulse energy 20 mJ and pulse duration less than 200 fs are expected to be achieved by adding two stages of traveling-wave amplification.