We experimentally demonstrate ultrafast dynamic of generation of the 337-nm nitrogen laser by injecting an external seed pulse into a femtosecond laser filament pumped by a circularly polarized laser pulse. In the pump-probe scheme, it is revealed that the population inversion between the C(3)Π(u) and B(3)Π(g) states of N(2) for the free-space 337-nm laser is firstly built up on the timescale of several picoseconds, followed by a relatively slow decay on the timescale of tens of picoseconds, depending on the nitrogen gas pressure. By measuring the intensities of 337-nm signal from nitrogen gas mixed with different concentrations of oxygen gas, it is also found that oxygen molecules have a significant quenching effect on the nitrogen laser signal. Our experimental observations agree with the picture of electron-impact excitation.