To meet the application requirements for high energy kHz repetition rate femtosecond laser, a high-efficiency femtosecond Ti:sapphire linear regenerative amplifier is designed. By optimizing the parameters of the cavity, 5.8 mJ chirped pulses at 800 nm are obtained, under pump energy of 20 mJ with wavelength of 527 nm at 1 kHz repetition rate, corresponding to a slope efficiency of 30.7%. By compensating for the dispersion, 4 mJ laser pulses at 800 nm with pulse duration of 45.7 fs are achieved. The energy fluctuation is 0.18% (RMS) in 5 h.