Summary: ``This paper is devoted to study dynamical behaviours of the fractional-order Bazykin-Berezovskaya model and its discretization. The fractional derivative has been described in the Caputo sense. We show that the discretized system, exhibits more complicated dynamical behaviours than its corresponding fractional-order model. Specially, in the discretized model Neimark-Sacker and flip bifurcations and also chaos phenomena will happen. In the final part, some numerical simulations verify the analytical results.''