Long Term Evolution (LTE) was initially designed for a high data rates network. However, voice service is always a main service that drives huge profits benefit for mobile phone operators. Hence the deployment of Voice over LTE (VoLTE) is very essential. LTE network is a fully All-IP network, thus, the deployment of VoLTE is quite complex, specially for guaranteeing of Quality of Service (QoS) for meeting quality of experience of mobile users. The key purpose of this paper is to present an object, non-intrusive prediction model for VoLTE quality based on Random Neural Network (RNN). In order to simulate an experiment, a three-layer feed-forward RNN architecture with gradient descent training algorithm is applied. The inputs of this model are object network impairments such as Packet Loss Rate (PLR), Delay and Jitter. The VoLTE quality was predicted in term of the Mean Opinion Score (MOS). The simulation results show that this model offers MOS values which are quite close to well-known method is WB-PESQ (Wideband Perceptual Evaluation of Speech Quality) model. The results also show that the proposed model is very suitable for predicting voice quality over LTE network.