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This paper addresses the issue of call admission control with the necessary QoS guarantee for a voice/data integrated wireless cellular network. Specifically, we propose a new call admission control policy called dual-threshold call admission control (DT-CAC) policy. It uses two thresholds, one to reserve channels for narrow-band voice handoff calls, and the other for wideband data handoff traffic. Its unique features are: (1) it adopts the complete sharing (CS) approach that maximizes the channel efficiency; (2) it derives the optimal set of thresholds that satisfies the QoS target on handoff dropping probabilities for both voice and data traffic, while at the same time minimizing the maximal new call blocking probability (voice or data). Its performance is well supported by simulation results.