In this paper the authors give an efficient bounded distance decoding (BDD for short) algorithm for NTRU lattices under some conditions about the modulus number q and the public key h.They then use this algorithm to give plain-text recovery attack to NTRU Encrypt and forgery attack on NTRU Sign.In particular the authors figure out a weak domain of public keys such that the recent transcript secure version of NTRU signature scheme NTRUMLS with public keys in this domain can be forged.