Researchers in biomedical optics use either the photon diffusion model or the Monte Carlo simulation to approach the `forward problem' of image reconstruction of the optical diffusion tomography for turbid media. Solving the photon transport equation is an alternate method to solve the `forward problem,' and might be more accurate because light propagation in turbid media is supposed to be better depicted by the photon transport equation than the other two methods. A solution to the time-dependent integro-differential equation has been found, using a hybrid (finite-difference and analytic) method. When the spatial and directional distributions of the initial light beam are given, analytical solutions to the photon transport equation are obtained for following discrete instances. This new approach has potential application to the time-resolved optical diffusion tomography as a more accurate solution to the `forward problem.'