The line width of pulsed quantum cascade lasers(QCL) increases with the device heating up during the driving pulse, so QCL drivers need to generate ultra-short current pulse. Generally, pulses of 5 ns to 15 ns durations can reach the Fourier transform limit. However, due to the existence of parasitic parameters, narrow pulses will lead to overshoot or oscillation. Therefore, the current commercial QCL drivers can not meet this requirement. To obtain narrower line width of QCLs, a frequency compensation method based on conventional pulse constant current circuit was proposed in this work to eliminate overshoot and oscillation. And a stable pulse laser driving circuit was also designed which can output 0-2 A pulse current, with 8.4-200 ns pulse width, <4 ns rising time, and <1%overshoot. Function test was carried out with a QCL with 4.6 μm center wavelength made from Institute of Semiconductor of ChineseAcademy of Sciences, and a Fourier transform infrared spectroscopy. The laser line width decreased almost linearly from 0.35 cm-1 to 0.12 cm-1, when the driving pulse width decreased from 100 ns to 10 ns. Experimental results show that the driver is able to output stable narrow pulses, which is suitable for narrow line width driving of QCLs and their applications.