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We use the Monte Carlo method to study an antiferromagnetical Ising spin system on a centred honeycomb lattice, which is composed of two kinds of 1/2 spin particles A and B. There exist two different bond energies JA-A and JA-B in this lattice. Our study is focused on how the ratio of JA-B to JA-A influences the critical behaviour of this system by analysing the physical quantities, such as the energy, the order parameter, the specific heat, susceptibility, etc each as a function of temperature for a given ratio of JA-B to JA-A. Using these results together with the finite-size scaling method, we obtain a phase diagram for the ratio JA-B / JA-A. This work is hclpful for studying the phase transition problem of crystals composed of compounds.