Internet pricing schemes have not been concerned in the network-neutrality research. In this paper, we study the implication of non-neutrality on the competition between Internet Access Providers. We interpret non-neutral network when a service provider privileges a Content Provider (CP) in order to propose a high quality of service for this content like time-sensitive applications (voice over Internet protocol, live video streaming, online gaming). We present a competitive model that describes the interaction between several competing telecommunications Access Providers (APs), their subscribers, and a network owner. Competition between the access providers is assumed to take place in their pricing decisions as well as in terms of the Quality of Service (QoS) they offer. Furthermore, our work focuses on the analysis of games between APs under two cases : case of neutral network and case of non-neutral network. After having discussed the existence and uniqueness of equilibrium, we analyzed the impact of non-neutrality versus neutrality. In particular, we showed that non-neutrality has a significant effect on the charged tariffs and the perceived quality of services in case where exist restrictions on the available bandwidth at the AP-CP link.