It is essential to guarantee a handoff dropping probability below a predetermined threshold for wireless mobile networks. Previous studies have proposed admission control policies for integrated voice/data traffic in wireless mobile networks. However, since QoS has been considered only in terms of CDP (Call Dropping Probability), the result has been a serious CBP (Call Blocking Probability) unfairness problem between voice and data traffic. In this paper, we suggest a new admission control policy that treats integrated voice and data traffic fairly while maintaining the CDP constraint. For underprivileged data traffic, which requires more bandwidth units than voice traffic, the packet is placed in a queue when there are no available resources in the base station, instead of being immediately rejected. Furthermore, we have adapted the biased coin method concept to adjust unfairness in terms of CBP. We analyzed the system model of a cell using both a two-dimensional continuous-time Markov chain and the Gauss-Seidel method. Numerical results demonstrate that our CAC (Call Admission Control) scheme successfully achieves CBP fairness for voice and data traffic.