Machine Type Communications (MTC) are automated applications which involve machines or devices that communicate through a network without any human intervention. They can be used today in almost everyday life applications from military to civil applications, such as: transportation, health care, smart energy, supply and provisioning, city automation... Those devices are generally spread in a wide area and should communicate through widely deployed networks. A good candidate to play the role of such a network could be cellular mobile networks. In fact, Cellular networks have been already deployed and o er a large coverage. Such a deployment is bene ficial for both mobile network Operators (i.e. more revenues) and the application developers (i.e. more opportunities). Furthermore, LTE networks are all-IP networks and off er a good support for MTC. However, cellular networks are not designed for MTC applications. Consequently, such a deployment is challenging and rises new problems. The most important of them is congestion. In fact, in MTC, a huge number of devices are deployed. This leads to contention and congestion in the the di fferent parts and nodes of the network when a lot of devices communicate at the same time. In the present work, we propose a novel Congestion-Aware Admission Control solution, which deals with the congestion in LTE networks. Our solution, which is based on control theory, e ffectively allows avoiding the core network congestion while saving the wireless scarce resources. We show its e ffectiveness through network simulations carried on the ns-3 simulator. In fact, the obtained results show that our solution is robust against di fferent traffic patterns and accommodates huge amount of devices as expected in this particular case of MTC applications. It assures a targeted utilization of the resources in the network. Furthermore, it is completely compliant with the actual protocols and standards.