In order to develop a high repetition rate X-ray lasers, the longitudinal-pumped transient collisional excitation (TCE) X-ray laser is one of the most effective pumping schemes. The high directive Ni-like Mo 18.9 nm soft X-ray laser pumped by modest laser energy has already been demonstrated by using the tabletop size Ti:sapphire/Nd:glass laser system that delivering energy of 150 mJ in 475 fs at the center wavelength of 1054 nm. The total energy in the pre-pulse and the main pulse was 150 mJ, which will make possible multi-hertz operation. To pursue the high repetition rate of the laser-driven TCE X-ray laser, we have designed a new 20 TW Ti:Sapphire laser system (600 mJ, 30 fs, 10 Hz). Special attention was paid to improve the contrast ratio, control of pulse shape as well as phase by an acoustic optic programmable dispersive filter (AOPDF) and 1 kHz preamplifier. Preliminary data have shown good laser characteristics. As the preliminary experiments, we have investigated high order harmonics generation from low-density laser plasma by using the solid target irradiated by a femtosecond laser pulse. The highest order was the 51st. harmonic at wavelength of 15.61 nm.