Purpose: The aim of this study was to develop novel methods for photoacoustically determining the optical absorption coefficient of biological tissues using Monte Carlo (MC) simulation. Methods: In this study, the authors propose two quantitative photoacoustic tomography (PAT) methods for mapping the optical absorption coefficient. The reconstruction methods combine conventional PAT with MC simulation in a novel way to determine the optical absorption coefficient of biological tissues or organs. Specifically, the authors' two schemes were theoretically and experimentally examined using simulations, tissue-mimicking phantoms, ex vivo, and in vivo tests. In particular, the authors explored these methods using several objects with different absorption contrasts embedded in turbid media and by using high-absorption media when the diffusion approximation was not effective at describing the photon transport. Results: The simulations and experimental tests showed that the reconstructions were quantitatively accurate in terms of the locations, sizes, and optical properties of the targets. The positions of the recovered targets were accessed by the property profiles, where the authors discovered that the off center error was less than 0.1 mm for the circular target. Meanwhile, the sizes and quantitative optical properties of the targets were quantified by estimating the full width half maximum of the optical absorption property. Interestingly, for the reconstructed sizes, the authors discovered that the errors ranged from 0 for relatively small-size targets to 26% for relatively large-size targets whereas for the recovered optical properties, the errors ranged from 0% to 12.5% for different cases. Conclusions: The authors found that their methods can quantitatively reconstruct absorbing objects of different sizes and optical contrasts even when the diffusion approximation is unable to accurately describe the photon propagation in biological tissues. In particular, their methods are able to resolve the intrinsic difficulties that occur when quantitative PAT is conducted by combining conventional PAT with the diffusion approximation or with radiation transport modeling.