In this paper, we present a new Call Admission Control (CAC) for IEEE 802.16 broadband wireless networks considering Quality of Service (QoS) constraint. With the assumption that there is a scheduling algorithm to allocate total bandwidths, our proposed CAC algorithm accepts new request for some slot times temporary. In this algorithm, during certain time slots, departure rate for ongoing connections will be decreased and for new connection will increase. After this period, if QoS for ongoing connections and new request is satisfied, new request will be accepted permanently and otherwise it will be rejected. We study the results in two phases, first we show that our algorithm works well with some routine scheduling algorithms and second we show the performance of our algorithm in comparison to some other CAC algorithms. We simulate our algorithm with Matlab tools, and the results show proposed algorithm is quite efficient.