A model employing five energy levels and a fit time-varying linear increase of photon pumping rate of X-ray source is proposed to analyze the gain of inner-shell photoionization (ISPI) X-ray laser in C. The deduced analytical expressions for the time of the onset of the peak gain and its peak value reveal the effects of Auger decay, electron impact ionization, the density of lasing medium and the increase rate of pumping rate on the duration and peak value of the laser gain. The requirement on the intensity of the driving ultra short pulse (USP) laser is estimated and the effect of changing the USP laser pulse duration on the peak gain is also given in this paper. Moreover, the model is used to estimate the requirements on the driving USP laser for ISPI X-ray laser in N.