In this article, trajectory equations of a relativistic electron and gain function of a free-electron laser in the presence of a counter propagating linearly polarized laser undulator embedded in an uniform guide magnetic field have been presented. Such a scheme produce very short wavelength and can be considered as a source of x-ray pulses which is easily tunable and highly monochromatic. A detailed analysis of gain function of laser-pumped FEl has been presented and numerical solutions of gain of the system, for group I and II orbits have been demonstrated and discussed.