Early problem in the issue of connecting separate physical networks to form one logical network was solved by packet-switching method for information. A Virtual Private Network (VPN) is a secured way of connecting a Local Area Network (LAN) to another in a remote location, using the packet-switching technology. VPN protocol encapsulates network data transfers using a secured cryptographic method between two or more networked devices. It keeps the data private when it passes through the connecting nodes. Quality of service(QoS) connections require the existence of routing mechanisms with least cost, delay & failures. This is achieved by providing, a set of alternative paths for each primary QoS path. This needs a guaranteed of Adjustment Restoration Algorithm (ARA). This research work has generated a 14 steps ARA, based on Barabasi-Albert Model Topology for a Network Size of 10 Nodes, using the Growth Attachment Mechanism. For comparison/evaluation, Waxman and Barabasi-Albert Models are used, with Symmetric & Asymmetric cases. In this tested and implemented model, the cost & delay are significantly smaller, quality of service constraints & delay factor is better than other models.