This paper introduces a new call admission control (CAC) mechanism for Long Term Evolution (LTE) networks supporting multimedia services with different classes of traffic. Our CAC mechanism classifies calls into real time and non-real time users, then estimates the channel quality based upon the received signal strength (RSS) value, and finally identifies the call as either new call (NC) or handoff call (HC) request before performing admission control decision. We also use a simple preemption technique in order to allocate the resources to high priority bearer requests. We show through extensive simulation analysis that our CAC mechanism provides high number of accepted users with higher priorities while providing high system throughput.