In this paper we present Monte Carlo studies of intensity modulated radiation therapy using laser-accelerated proton beams. Laser-accelerated protons coming out of a solid high-density target have broad energy and angular spectra leading to dose distributions that cannot be directly used for therapeutic applications. Through the introduction of a spectrometer-like particle selection system that delivers small pencil beams of protons with desired energy spectra it is feasible to use laser-accelerated protons for intensity modulated radiotherapy. The method presented in this paper is a three-dimensional modulation in which the proton energy spectrum and intensity of each individual beamlet are modulated to yield a homogeneous dose in both the longitudinal and lateral directions. As an evaluation of the efficacy of this method, it has been applied to two prostate cases using a variety of beam arrangements. We have performed a comparison study between intensity modulated photon plans and those for laser-accelerated protons. For identical beam arrangements and the same optimization parameters, proton plans exhibit superior coverage of the target and sparing of neighbouring critical structures. Dose-volume histogram analysis of the resulting dose distributions shows up to 50% reduction of dose to the critical structures. As the number of fields is decreased, the proton modality exhibits a better preservation of the optimization requirements on the target and critical structures. It is shown that for a two-beam arrangement (parallel-opposed) it is possible to achieve both superior target coverage with 5% dose inhomogeneity within the target and excellent sparing of surrounding tissue.