Recently, multimedia communication by smart-phones and tablets via mobile networks have become popular in daily life. Therefore, an effective method to use the limited wireless resources is necessary. When using wireless resources among multiple users, the schedulers allocate resources to each user. When allocating resources, assuring quality of experience (QoE) and achieving high system throughput are fundamental. In this paper, we present a two-step radio resource allocation algorithm for the downlink of a long term evolution (LTE) network, by taking into account the user's and the service provider's perspective. At the first step, it allocates resources dynamically to each user so that a minimum QoE is guaranteed for every user. In the second step, it allocates resources dynamically to improve the system throughput while achieving a high-level of QoE. We show that our proposed algorithm achieves a higher level of QoE than the conventional allocation algorithms based on quality of service (QoS) metrics, as well as a higher throughput compared to the conventional allocation algorithms based on QoE.