In this paper we use a bond-operator mean-field theory to study the quantum phase transition in the bilayer Heisenberg antiferromagnet. The obtained critical point and low temperature quantum critical behavior are consistent with the numerical results and the nonlinear σ model results. In the very low temperature (T≤0.3J1, J1 is the in-plane antiferromagnetic coupling), where the numerical results are not available, present paper gives new evidence for the quantum critical behavior.