We have developed one-and a half-dimensional (one space dimension and two velocity components) relativistic electromagnetic cloud-in-cell simulation (CIC-R) code which is suitable for simulating the free-electron laser process. Using CIC-R we have simulated the temporal evolution of the free-electron laser, and obtained the results on the linear growth rates of the unstable spectrum and the dispersion relation of the coupling between the electromagnetic waves and electrostatic waves which agree with the theory. Other results such as the time development of the electron distribution function, nonlinear saturation and the efficiency of energy conversion are also presented in detail.