Negative sequential patterns (NSP) are critical and sometimes much more informative than positive sequential patterns (PSP) in many intelligent systems and applications. However, the existing NSP algorithms do not allow negative items being contained in an element except the NegI-NSP algorithm, which can obtain many meaningful sequences with negative items in an element. NegI-NSP, however, hasn’t considered the following problems: (1) it uses a single minimum support to all size sequences, which is unfair to a long size sequence; (2) it only mines NSP from PSP, not from infrequent positive sequences (IPS), which also contain many useful NSP. So we propose an efficient algorithm, named MLMS-NSP, to mine NSP based on multiple level minimum supports (MLMS) from PSP and IPS. Firstly, MLMS scheme is proposed by assigning different minimum supports to sequences with different sizes. Secondly, IPS are constrained by combining MLMS, and then the NSP is obtained from these IPS. Finally, experimental results show that the MLMS-NSP algorithm can effectively mine NSP from IPS, and the time efficiency is higher than using single minimum support,