Optimizing the balance between different handover parameters for network selection is one of the challenging tasks for seamless communication in heterogeneous networks. Traditional approaches for network selection are mostly based on the Receive Signal Strength (RSS) from the Point of Attachment (PoA) of a network. Most of these schemes are suffered from high handover delay, false handover indications, and inappropriate network selection for handover. To address these problems, we present an optimized network selection scheme based on the speed of a mobile node. A mechanism based on two different thresholds on the speed of a Mobile Node (MN) is integrated in the proposed scheme. If the speed of an MN is greater than any of the threshold, the MN performs handover to a particular network. We employ Grey Relational Analysis (GRA) in the proposed scheme to select the best PoA of the selected network. Similarly, to deal with false handover indications, we proposed an optimized handover triggering technique. We compare our proposed scheme with existing schemes in context of energy consumption for scanning, frequent and failed handovers, packet loss ratio, and handover delay. The proposed scheme shows superior performance and it outperforms existing schemes used for similar purpose. Moreover, simulation results show the accuracy and performance of the proposed scheme.