The mobile cloud services can be accessed over an internet by portable devices. The rapid growth of mobile services and cloud computing, the Mobile Cloud Computing becomes so popular. Mobile Cloud Computing (MCC) incorporates the cloud computing technology with mobile environment. The service associated with quality of service parameters which make it preeminent service to a user. This paper proposed a Preeminet Service Ranking (PSR) method using backward propagation neural network (BPNN) to find the best services. The method consists of two phases which are the Training phase and the Ranking phase. In the Training phase, the network is trained and obtain the deviation. It means that error of the current network from the ideal network. In the Ranking phase, determine the best services are at any given time using the deviation obtained from the training phase. The mobile cloud services are measured by using Quality of Service (QoS) parameters. This paper proved that a proposed method performs better over conventional methods like TOPSIS, AHP, and ANP. © 2018 The Authors. Published by Elsevier Ltd.