MIRAX (Monitor e Imageador de Raios X) is a satellite mission designed to monitor the hard X-ray and soft gamma-ray part of the sky (5 - 200 keV). Its principal instrument is an X-ray camera that makes use of a coded mask and solid-state (CZT) detectors. With its wide field of view (20 20 degrees) MIRAX will study variable sources such as accreting neutron stars (NS), black holes (BH), active galactic nuclei and both short and long gamma-ray bursts (GRBs). In this work we present an estimation on how many GRBs MIRAX will be able to detect during its low-earth near equatorial orbit (90 min). We perform Monte Carlo simulations with GEANT4 to reproduce the interaction of the cosmic diffuse background with the detector material, and image reconstructions for different known GRB sources at different positions in the field of view. We also compute MIRAX sensitivity curve over the energy detection range, and estimate the redshift range for which a GRB will be detectable by MIRAX as a function of the flux.