The proliferation of mobile devices and user applications has continued to contribute to the humongous volume of data traffic in cellular networks. To surmount this challenge, service, and resource providers are looking for alternative mechanisms that can successfully facilitate managing network resources in a more dynamic, predictive, and distributed manner. New concepts of network architectures, such as software-defined network (SDN) and network function virtualization (NFV), have paved the way to move from static to flexible networks. They make networks more flexible (i.e., network providers capable of ondemand provisioning), easily customizable, and cost effective. In this regard, network slicing is emerging as a new technology built on the concepts of the SDN and NFV. It splits a network infrastructure into isolated virtual networks and allows them to manage resources allocation individually based on their requirements and characteristics. Most of the existing solutions for network slicing are computationally expensive because of the length of time they require to estimate the resources required for each isolated slice. In addition, there is no guarantee that the resource allocation is fairly shared among users in a slice. In this paper, we propose a network slicing resource management (NSRM) mechanism to assign the required resources for each slice in a LTE network, taking into consideration the isolation of resources among different slices. In addition, NSRM aims to ensure isolation and fair sharing of distributed bandwidths between users belonging to the same slice. In NSRM, depending on requirements, each slice can be customized (e.g., each can have a different scheduling policy).