We introduced a weak prepulse 0-2 ns before the main pulse in the formation of a terahertz (THz) wave in air plasma by laser pulses composed of fundamental and second-harmonic waves. The prepulse suppressed the THz wave generated by the main pulse. We analyzed the suppression factor as a function of the time interval between the prepulse and the main pulse and found that the THz wave from the main pulse decreases immediately after the prepulse, recovers partially within several hundred picoseconds, and then recovers slowly. This suppression is attributed to the dense plasma, which absorbs and screens the generated THz wave, since the relaxation time is close to the lifetime of the fluorescence from the plasma. The results support the idea that the major mechanism of THz wave generation is explained by the plasma current model.