In wireless cellular environment the handoff algorithm determine when the handoff will occur and at which base station. Heterogeneous network such as UMTS, WLAN, WiMax where vertical hand off is required further challenges the cellular network. This paper provides an adaptive multiple attribute vertical hand of algorithm which allows wireless networks to select a mobile terminal using fuzzy logic concept. The main contribution of this paper is to propose adaptive data rate oriented speed and capacity based vertical hand of schemes which not only considers velocity, signal strength but also considers network bandwidth utilization for achieving load balancing named as adaptive data rate adjustment. This enables the user in achieving quality of service in heterogeneous network and provides free moving experience. A performance study using heterogeneous network such UMTS, WLAN, WiMax, as example shows that our proposed vertical hand off algorithm is able to determine when the hand off is required and selects the best access network that is optimized to network conditions , quality of service requirement , user preference , service cost , mobile terminal conditions .