Providing seamless connectivity in heterogeneous wireless networks has been a challenging job for the last couple of years. Traditional Vertical Handover Management (VHM) schemes are not enough good, to support seamless connectivity in heterogeneous networks. Therefore, to deal with the challenges such as inappropriate handover triggering and network selection, we propose a multi-criteria based VHM scheme. The handover triggering is based on the data rate required by the number of applications running on a mobile node's device. A threshold is defined on the lowest possible data rate requirement for each application. Similarly, the network selection is carried using the Grey Relational Analysis (GRA) decision scheme based on delay, jitter, bandwidth, communication cost, and network load. The proposed scheme is tested on a number of mobility scenarios with three different networks WIFI, WiMAX, and LTE (cellular). Similarly, the proposed scheme is simulated against the periodic, adaptive scanning, and IEEE 802.21; Media Independent Hanover (MIH) standard. The proposed scheme shows superior performance and it outperforms existing schemes used for a similar purpose.