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The architecture for the Beyond 3rd Generation or 4th Generation wireless networks aims at integrating various heterogeneous wireless access networks over an IP backbone. To provide seamless mobility, one of the design issues is the vertical handoff support. In this paper, we propose a SINR(Signal to Interference plus Noise Ratio) and AHP(Analytic Hierarchy Process) based SAW(Simple Additive Weighting)(SASAW) vertical handoff algorithm which uses the combined effects of SINR, user required bandwidth, user traffic cost and available bandwidth of the participating access networks to make handoff decisions for multi-attribute QoS consideration according to the features of the traffic. The results show that our proposed scheme can achieve excellent performance according to the characteristics of the traffic by considering the relations of multiple attributions synthetically.