With the development of mobile communications and the Internet of Things, non-orthogonal multiple access (NO-MA) may be one of the candidates for 5G. In the uplink NOMA system, there are a large number of connected users with multiuser detection, fewer active users and sparse signals in a certain time duration. In this paper, we propose a compressive sensing based multi-user interference cancellation (CS-IC) method to detect the active users and data of the grant-free non-orthogonal multiple access (GF-NOMA) system. It greatly reduces the signaling overhead and control transmission delay, because the active users do not send the active status information to the base station and do not need to interact with the base station in advance. Simulation results show that the proposed CS-IC multiuser detection can obtain much better BLER performance than the IC and MMSE-IC multi-user detection, greatly improving the spectrum efficiency.