Free-electron lasers (FEL) are the brightest, coherent sources of short wavelength radiation from the VUV into the x-ray. There is much research interest in reducing the cost and the size of FELs by utilising new accelerator techniques. Laser-plasma accelerator (LPA) are a promising accelerator for next generation compact FEL light sources with many potential advantages due to the high acceleration gradient and large peak currents they offer. The electron beams of a LPA typically have a smaller transverse emittance, a large energy spread and tend to be of shorter duration and higher current than conventional Radio Frequency (RF) accelerators. In this paper, a FEL driven by an electron beam from a typical LPA was simulated using the 3D FEL simulation code Puffin. It is shown that lowering the homogenous electron beam energy spread increases the radiation energy output in a short undulator and , as become less than the FEL, or Pierce parameter (r), then the peak radiation energy increases and the saturation length reduces significantly as expected.