We describe a Ti:sapphire multi-pass amplifier with high efficiency at the repetition rate of 1 kHz. In the amplifier, the incident pulse is 0.66 mJ with the pulse duration about 90 ps. The incident pulse is amplified to 7.2 mJ when the pump energy is 23 mJ. The energy efficiency in the amplifier is nearly 30% with extracting efficiency larger than 40% when considering about 25% static reflecting loss in the amplifier. After compressed in the compressor, 5.4-mJ, 36-fs pulses with peak power larger than 0.1 TW are obtained.