We developed a compact Ti:sapphire laser amplifier system in our laboratory, generating intense laser pulses with a peak power of >1 TW (terawatt), a pulse duration of 34 fs (femtosecond), a central wavelength of 800 nm, and a repetition rate of 10 Hz. The laser amplifier system consists of a mode-locked Ti:sapphire oscillator, a regenerative amplifier, and a single-side-pumped 4-pass amplifier. The chirped-pulse amplification (CPA)-based laser amplifier was found to provide an energy of 49.6 mJ after compression by gratings in air, where the pumping fluence of 1.88 J/cm2 was used. The amplified spontaneous emission (ASE) level was measured to be lower than 10−7, and ps-prepulses were in 10−4 or lower level. The developed laser amplifier system was used for the generation of intense THz (terahertz) waves by focusing the original (800 nm) and second harmonic (400 nm) laser pulses in air. The THz pulse energy was shown to be saturated in the high laser energy regime, and this phenomenon was confirmed by fully electromagnetic, relativistic, and self-consistent particle-in-cell (PIC) simulations.