In this paper a simple and effective call admission control (CAC) scheme is proposed for the emerging interleave-division multiple-access (IDMA) systems, supporting a variety of traffic types and offering different quality of service (QoS) requirements and priority levels. The proposed scheme is signal-to-interference-plus-noise ratio (SINR) evolution based CAC (SE-CAC). The key idea behind the scheme is to take advantage of the SINR evolution technique in the process of making admission decisions, which is developed from the effective chip-by-chip (CBC) multi-user detection (MUD) process in IDMA systems. By virtue of this semi-analytical technique, the MUD efficiency can be estimated accurately. Additionally, the computational complexity can be considerably reduced. These features make the scheme highly suitable for IDMA systems, which can combat intra-cell interference efficiently with simple CBC MUD. Analysis and simulation results show that compared to the traditional CAC scheme considering MUD efficiency as a constant, the proposed SE-CAC scheme can guarantee high power efficiency and throughput for multimedia traffic even in heavy load conditions, illustrating the high efficiency of CBC MUD. Furthermore, based on the SINR evolution, the SE-CAC can make accurate estimation of available resource considering the effect of MUD, leading to low outage probability as well as low blocking and dropping probability.