A symbol‐asynchronous uplink non‐orthogonal multiple access (NOMA) model is considered, where K users transmit codewords to a common receiver according to their local clocks. As the complicated user location and the dynamic transmission environment, the exact time offsets of users are not always available at the base station (BS). To ensure the efficiency of the system, linear minimum mean square error algorithm and partial message passing (P‐MP) algorithm are designed based on iterative detection. The signal to interference plus noise ratio is also applied to analysis the effect of estimated time offsets on the P‐MP algorithm. Then simulation results show that when the variance of estimation error is 0.1, the symbol‐asynchronous NOMA systems with imperfect time offsets can achieve the same or even better bit error rate performance than the NOMA system.