The spin-12 Heisenberg antiferromagnet on the distorted honeycomb (DHC) lattice is studied by means of the tensor renormalization-group method. It is unveiled that the system has a quantum phase transition of second order between the gapped quantum dimer phase and a collinear Néel phase at the critical point of coupling ratio $α$c$∼eq$0.54, where the quantum critical exponents $ν∼eq$0.69(2) and $γ∼eq$1.363(8) are obtained. The quantum criticality is found to fall into the O(3) universality class. A ground-state phase diagram in the field-coupling ratio plane is proposed, where the phases such as the dimer, semiclassical Néel, and polarized phases are identified. A link between the present spin system to the boson Hubbard model on the DHC lattice is also discussed.