Modern real-time wireless networks require high security level to assure confidentiality of information stored in packages delivered through wireless links. However, most existing algorithms for scheduling independent packets in real-time wireless networks ignore various security requirements of the packets. Therefore, in this paper we remedy this problem by proposing a novel dynamic security-aware packet-scheduling algorithm, which is capable of achieving high quality of security for realtime packets while making the best effort to guarantee realtime requirements (e.g., deadlines) of those packets. We conduct extensive simulation experiments to evaluate the performance of our algorithm. Experimental results show that compared with two baseline algorithms, the proposed algorithm can substantially improve both quality of security and real-time packet guarantee ratio under a wide range of workload characteristics.