[en] Compton scattering between an intense laser pulse and a relativistic electron beam offers a promising development path toward high-energy, high-brightness x- and gamma-ray sources. Increasing laser peak power to obtain intense x- and gamma rays causes nonlinear Compton scattering to occur. To predict high-order harmonic radiation properties, we upgrade a Monte Carlo laser-Compton scattering simulation code (MCLCSS) by taking into account the nonlinear effect for the relativistic Compton scattering process. The energy spectra and angular and harmonic intensity distributions of the scattered photons are investigated using nonlinear Compton scattering of an intense circularly polarized laser. It is found that the laser parameter a₀≡eA m_ec⁻² plays an important role in the generation of high-order harmonic radiation. Our study also suggests that the high-energy tails of the second and higher harmonics will stray from the backscattering region. (papers)