We present 30 fs pulse duration home-made chirped pulse amplification Ti:sapphire laser system operating at a repetition rate of 1 kHz with 4.0 mJ pulse energy. The Ti:sapphire laser system with ım819 nm center wavelength has a long-cavity oscillator, four pass grating stretcher, 8-pass pre-amplifier, 4-pass post-amplifier and a double pass grating compressor. The Peltier coolers and thermal eigenmode post-amplifier are introduced to compensate the thermal lensing of the crystal in the amplifiers and to enhance the beam focusability on the crystal. The Strehl ratio and M² value measured by employing the Shack-Hartman wavefront sensor HASO4 to observe the spatial profile and beam quality. The most sensitive single-shot second harmonic generation frequency-resolved optical gating diagnostic technique is employed to characterize intensity and phase of the output compressed laser pulses.