The diamond-amplifier photocathode (DAP) offers a new widely applicable way to generate high average-current, high brightness, and low thermal emittance electron beams. Physical processes with multiple parameters are important for the design of a reliable and efficient DAP. To perfom a study in-depth, a 2D Monte Carlo model in MATLAB frame is built to simulate the secondary electron transport in diamond. This simulation gives some proofs that the drift velocity is sensitive to diamond temperature and electric field applied, but not sensitive to the low impurity density(<10^{17}/cm^{-3}). As an appropriate result, the saturation velocity of secondary electron reaches 1.88?10^{7} cm/s, and mobility without applied field is 3732 cm^{2} /V.s. In addition, some properties of a secondary electron bunch transported in diamond are discussed, which indicate that the effect of space charge under our considered electron cloud density is small.