The nucleotide base-pairing in DNA replication and proteins synthesis can be looked as an unsorted database search. Compared to the classical search, the quantum search was square root accelerated. Based on the classical coupled harmonic oscillators system, which corresponds to Grover quantum search algorithm, and quantum tunneling effect, the model of the nucleotide base selection and H-bond formation was proposed. In addition, the catalysis of the DNA polymerase was discussed from the point of view of quantum coherence maintained. Finally, the optimization of biological information processing through the point of informatics was proved.