to the different services in mobile broadband networks (WiMAX, LTE). A new connection is admitted only when the network can support the QoS needs of the connection without degrading the QoS for existing connections. An efficient call admission control algorithm ensures higher throughput and fewer delays for the admitted connections. In this paper a graded priority-based call admission control algorithm is proposed for LTE and WiMAX networks. The number of permissible connections shall be segregated into two classes. The new connection shall be graded, prioritized, and admitted based on the device requesting the connection. Simulation results show that graded priority-based admission control algorithm improves the connection admission rate from 3{\%} to as high as 30{\%} for select users. This results in higher throughput for priority users.