We have stabilized the carrier-envelope phase (CEP) of amplified femtosecond laser pulses from a grating-based chirped-pulse amplification femtosecond laser by the direct locking method. Long-term CEP stabilization in the oscillator was achieved by employing a double-feedback loop to control both the pumping power and the cavity dispersion. Large CEP drift, induced during amplification, was compensated by adjusting the grating separation in the pulse compressor, and the CEP stabilization was maintained for four hours with a phase jitter of about 180 mrad. After pulse compression to 5.5-fs pulses in a filamentation pulse compressor, CEP-stabilized laser pulses were applied for high-harmonic generation to confirm the CEP stabilization.