This study is focused on the pressure blow-up criterion for a smooth solution of three-dimensional zero-diffusion Boussinesq equations. With the aid of Littlewood-Paley decomposition together with the energy methods, it is proved that if the pressure satisfies the following condition on margin Besov spaces,π(x,t)∈L2/(2+r)(0,T;B˙∞,∞r)forr=±1,then the smooth solution can be continually extended to the interval(0,T⁎)for someT⁎>T. The findings extend largely the previous results.