Quantum cryptography and quantum search algorithm are considered as two important research topics in quantum information science.An asymmetrical quantum encryption protocol based on the properties of quantum one-way function and quantum search algorithm is proposed.Depending on the no-cloning theorem and trapdoor one-way functions of the publickey,the eavesdropper cannot extract any private-information from the public-keys and the ciphertext.Introducing key-generation randomized logarithm to improve security of our proposed protocol,i.e.,one privatekey corresponds to an exponential number of public-keys.Using unitary operations and the single photon measurement,secret messages can be directly sent from the sender to the receiver.The security of the proposed protocol is proved that it is informationtheoretically secure.Furthermore,compared the symmetrical Quantum key distribution,the proposed protocol is not only efficient to reduce additional communication,but also easier to carry out in practice,because no entangled photons and complex operations are required. Quantum cryptography and quantum search algorithm are considered as two important research topics in quantum information science. An asymmetrical quantum encryption protocol based on the properties of quantum one-way function and quantum search algorithm is proposed. Decision on the no-cloning theorem and trapdoor one -way functions of the publickey, the eavesdropper can not extract any private-information from the public-keys and the ciphertext.Introducing key-generation randomized logarithm to improve security of our proposed protocol, ie, one privatekey correspond to an exponential number of public- keys.Using unitary operations and the single photon measurement, secret messages can be directly sent from the sender to the receiver. The security of the proposed protocol is proved that it is information theologically secure. Future, comparing the symmetrical Quantum key distribution, the proposed protocol is not only efficient to reduce additional communication, but also easier to carry out in practice, because no entangled photons and complex operations are required.