As a clinical application of an exciting scientific breakthrough, a compact and cost-efficient proton therapy unit using high-power laser acceleration is being developed at Fox Chase Cancer Center. The significance of this application depends on whether or not it can yield dosimetric superiority over intensity-modulated radiation therapy (IMRT). The goal of this study is to show how laser-accelerated proton beams with broad energy spreads can be optimally used for proton therapy including intensity-modulated proton therapy (IMPT) and achieve dosimetric superiority over IMRT for prostate cancer. Desired energies and spreads with a varying deltaE/E were selected with the particle selection device and used to generate spread-out Bragg peaks (SOBPs). Proton plans were generated on an in-house Monte Carlo-based inverse-planning system. Fifteen prostate IMRT plans previously used for patient treatment have been included for comparison. Identical dose prescriptions, beam arrangement and consistent dose constrains were used for IMRT and IMPT plans to show the dosimetric differences that were caused only by the different physical characteristics of proton and photon beams. Different optimization constrains and beam arrangements were also used to find optimal IMPT. The results show that conventional proton therapy (CPT) plans without intensity modulation were not superior to IMRT, but IMPT can generate better proton plans if appropriate beam setup and optimization are used. Compared to IMRT, IMPT can reduce the target dose heterogeneity ((D5-D95)/D95) by up to 56%. The volume receiving 65 Gy and higher (V65) for the bladder and the rectum can be reduced by up to 45% and 88%, respectively, while the volume receiving 40 Gy and higher (V40) for the bladder and the rectum can be reduced by up to 49% and 68%, respectively. IMPT can also reduce the whole body non-target tissue dose by up to 61% or a factor 2.5. This study has shown that the laser accelerator under development has a potential to generate high-quality proton beams for cancer treatment. Significant improvement in target dose uniformity and normal tissue sparing as well as in reduction of whole body dose can be achieved by IMPT with appropriate optimization and beam setup.