In the massive machine-type communication scenario, aiming at the problems of active user detection and channel estimation in the grant-free non-orthogonal multiple access (NOMA) system, new sets of non-orthogonal spreading sequences are proposed by using the zero/low correlation zone sequence set with low correlation among multiple sets. The simulation results show that the resulting sequence set has low coherence, which presents reliable performance for channel estimation and active user detection based on compressed sensing. Compared with the traditional Zadoff-Chu (ZC) sequences, the new non-orthogonal spreading sequences have more flexible lengths, and lower peak-to-average power ratio (PAPR) and smaller alphabet size. Consequently, these sequences will effectively solve the problem of high PAPR of time domain signals and are more suitable for low-cost devices in massive machine-type communication.