A novel construction method of cluster states quantum fuzzy hash utilizing classical-quantum ε-universal hashing family was proposed. Traditional hash and fuzzy hash algorithm are not effective against quantum attacks. Utilizing the method of diamond norm, an optimal subset of hash functions family was constructed and better security on the sense of information theory was guaranteed. Based on the unique physical one-way computation properties of quantum cluster states, the corresponding algorithm is more close to the physical realization. And then, a novel scheme of covert information search in the field of information security and biometrics was presented. The biometrics search algorithm is constructed from the cluster states quantum ε-universal fuzzy hashing. The algorithm can effectively resist the quantum algorithm attack, ensure data storage security and reduce the complexity. Compared to others similar schemes, the algorithm has a more simplified structure. Theoretical analysis shows that the algorithm has higher recognition efficiency and better data security.