We have demonstrated a carrier-envelope phase (CEP) stabilized chirped-pulse amplification (CPA) system employing a grating-based pulse stretcher and compressor and a regenerative amplifier for the first time. In addition to stabilizing the carrier-envelope offset phase of a laser oscillator, a new pulse selection method referenced to the carrier-envelope offset beat signal was introduced. The pulse-selection method is more robust against the carrier-envelope offset phase fluctuations than a simple pulse-clock dividing method. We observed a stable fringe in a self-referencing spectrum interferometry of the amplified pulse, which implies that the CEP of amplified pulse is stabilized. We also measured the effect of the beam angle change on the CEP of amplified pulses. The result demonstrates that the CEP stabilized CPA is scalable to higher-pulse energies.