We present a method of simulating the electron transport in low-temperature-grown GaAs by the Monte Carlo method. Low-temperature-grown GaAs contains microscopic inclusions of As and these inhomogeneities render impossible the standard Monte Carlo mobility simulations. Our method overcomes this difficulty and allows the quantitative prediction of electron transport on the basis of principal microscopic material parameters, including the impurity and the precipitate concentrations and the precipitate size. The adopted approach involves simulations of a single electron trajectory in real space, while the influence of As precipitates on the GaAs matrix is treated in the framework of a Schottky-barrier model. The validity of this approach is verified by evaluation of the drift velocity in homogeneous GaAs where excellent agreement with other workers' results is reached. The drift velocity as a function of electric field in low-temperature-grown GaAs is calculated for a range of As precipitate concentrations. Effect of compensation ratio on drift velocity characteristics is also investigated. It is found that the drift velocity is reduced and the electric field at which the onset of the negative differential mobility occurs increases as the precipitate concentration increases. Both these effects are related to the reduced electron mean free path in the presence of precipitates. Additionally, comparatively high low-field electron mobilities in this material are theoretically explained.