In this study, we use MCNP Monte Carlo method to optimize the design of Marinelli Beaker (MB) of BGO (Bi 4Ge 3O 12) crystal detector which occurs β + decay from the gas source and further produce positron and then positron-electron annihilation to produce γ ray. We first calculate the number of γ ray to determine the relation between the thickness of metal layer of BGO crystals detector and the peak value efficiencies. Our results show that the peak value efficiency arrive the maximum value point when the metal layer with thickness of 0.7 mm...