Lattice-based cryptosystems rely on certain lattice problems for their security,such as the shortest vector and the closest vector problems. NTR U is a kind of lattice-based public key cryptosysytem gaining much attention because of its high efficifency. Its encryption and decryption use a mixing system suggested by polynomial algebra combined with a clustering principle based on elementary probability theory. With the availability of quantum computers, the security of cryptosystems based on classical mathematic problens needs to be reevaluated. Since lattice reduction is the main threat to lattice-based cryptosystems, lattice reduction using quantum search algorithms are analyzed to evaluate the security of NTRU in this paper. Aceording to our results, original security parameters proposed for NTRU should be increased in the event that Grovers quantum search algorithm is used for lattice reduction.