To obtain narrower linewidth and more intense THz radiation, long-pulse and high-peak power optical pumping source is attempted by performing a light amplification experiment in which a 6 W tunable continuous-wave CO2 seeding laser is amplified by a double-pass amplifier with TEA CO2 laser. The result of an amplification factor of 30 at 14 μs pulse duration （FWHM） is obtained experimentally. During the amplification, the output power of the amplified light increases with that of seeding light increasing, especially for the CO2 10P （20）line. Based on the optical pumping source of long pulse laser, a dynamic model for generating pulsed THz radiation is established, and the expression of saturation pumping intensity which yields THz radiation is given, thus the range of pumping intensity can be determined. In addition, by solving time-dependent equation of dynamic model, the expression of pumping energy absorbed by THz medium is deduced. Theoretical analysis shows further that the heavy molecules will be more appropriate for THz gain medium for long pulse pumping source, and no THz radiation can be generated due to the absence of population reversion below pumping intensity.