Abstract-The Session Initiation Protocol (SIP) is an application-layer control protocol for creating, modifying and terminating multimedia sessions. An open issue is the control of overload that occurs when a SIP server lacks sufficient CPU and memory resources to process all messages. We prove that the problem of overload control in SIP network with a set of n servers and limited resources is in the form of NP-hard. This paper proposes a Load-Balanced Call Admission Controller (LB-CAC) based on a heuristic mathematical model to determine an optimal resource allocation in such a way that maximizes call admission rates regarding the limited resources of the SIP servers. In fact, LB-CAC by having some critical information of SIP servers determines the optimal "call admission rates" and "signaling paths" for admitted calls along optimal allocation of CPU and memory resources of the SIP servers through a new linear programming model. A comparison between the numerical and experimental results implies the efficiency of the proposed method.