Due to the rapid increase in internet users and quick development of real time services such as voice and video there is a high demand in quality of service given to the users. Therefore it seems it is necessary to go for next generations of cellular networks available all over the world. LTE is a new radio access technology suggested as a means to go for next generation of wireless systems. It uses an orthogonal frequency division multiplexing system. This system divides the bandwidth into several narrowband sub-channels and devotes the mentioned sub-carriers to the users regarding their needs. One of the main properties of LET is enjoying the advanced methods of radio resource management in order to optimize the performance of the system so that the number of the transmitted bits be the most. To give high quality of service to the users, there are scheduling algorithms designed to meet the user’s needs. scheduling in LTE networks is in charge of distributing the resources between active users to give proper quality of service. In these algorithms, the application of real time services are considered while in some of other algorithms applications of both real time and non-real time services are considered. In the latter algorithms, there is no emphasis on different velocities of users. In addition, these algorithms are only focused on users with slow velocities (Up to 30 km /h). However, it is important for an algorithm to give a proper quality of services even in high velocities. In this thesis, we have done our best to design an algorithm offering a proper quality of service to the users with different velocities and also increase the network throughput. Also, the algorithm is tried to have an acceptable performance comparing with other algorithms. Making a comparison between the results of simulations of the proposed algorithm with other algorithms reveals that the network throughput is increased in the proposed algorithm. Also, the quality of service parameters are enhanced. That’s mainly because of choose of proper Index for resource block allocation to the user. Keywords : LTE ,QoS ,Radio Resource Management ,Scheduling ,RT amRT Services