In this paper, the fading broadcast channel with confidential messages is studied in the presence of statistical quality of service (QoS) constraints in the form of limitations on the buffer length. We employ the effective capacity formulation to measure the throughput of the confidential and common messages. We assume that the channel side information (CSI) is available at both the transmitter and the receivers. Considering average power constraints at the transmitter side, we first define the effective secure throughput region, and prove that the throughput region is convex. Then, we obtain the optimal power control policies that achieve the boundary points of the effective secure throughput region.