N-Shift Zero Correlation Zone (NS-ZCZ) sequence is defined with the N-shift zero correlation zone in the correlation function. Namely, the N-shift zero only appears within the correlation zone symmetrically distributed in the center of the correlation function. Moreover, the traditional ZCZ sequences can be considered as the N-shift ZCZ sequence with N=1. Similar to ZCZ sequence, NS-ZCZ sequences can be applied in sequence design for co-channel interference mitigation with more sequences in the sequence set compared with the traditional N-shift sequences. In this letter, the definition and construction algorithms are proposed. The corresponding theoretical bounds are analyzed.