A one-dimensional model of free electron laser was presented through a computer simulation and Matlab 6.1 language. The FEL that had been used was amplifier with a helical undulator. The electron beam was suggested to be in two types of energy distribution regimes; uniform and lorentzian distribution. The work deals with the linear mode of operation. The electron behavior inside the undulator, the bunch formation, the effect of the space charge fields and the difference in energy between electrons on the field gain and the output power gain of the system were studied. It is found that the increase in the space charge fields_ causes decreasing in the output power gain of the Free Electron Laser because these fields will leads to less chance for the formation of the electron bunches along the undulator length or it will be formed for a short time so that the radiation obtained from these bunches will be small and this will affect on the output power of the FEL system. It is also found that the difference in energy between the electrons that had been inserted inside the undulator causes decreasing in the output power gain because a small portion of these electrons will leads to the successive amplification process. This result was obtained by taking several values for the parameter that represents this difference.