The magnetic properties and phase diagrams of the mixed spin-1/2 and spin-1 Ising model on a honeycomb inside a hexagonal structure have been studied using the Monte Carlo simulations based on the Metropolis update protocol. The effect of different exchange interactions (intralayer and interlayer Js') and single-ion anisotropy D on the magnetic properties, transition and compensation temperatures, and magnetic susceptibility have been investigated. The phase diagrams, T-J and T-D, for different exchange interactions and crystal field values have been examined. Compensation behavior exists for critical values of interlayer's exchange interactions. Our calculations reveal the existence of two points of compensation for a narrow range of negative D. Article highlights A mixed spin Ising model on a centered honeycomb-hexagonal structure was proposed The effects of crystal field and exchange coupling were studied Two points of compensation temperature were exist.