The next generation electrical power grid, known as smart grid (SG), requires a communication infrastructure to gather generated data by smart sensors and household appliances. Depending on the quality of service (QoS) requirements, this data is classified into event-driven (ED) and fixed-scheduling (FS) traffics and is buffered in separated queues in smart meters. Due to the operational importance of ED traffic, it is time sensitive in which the packets should be transmitted within a given maximum latency. In this paper, considering QoS requirements of ED and FS traffics, we propose a two-stage wireless SG traffic scheduling model, which results in developing a SG traffic scheduling algorithm. In the first stage, delay requirements of ED traffic is satisfied by allocating the SG bandwidth to ED queues in smart meters. Then, in the second stage, the SG rest bandwidth is going to the FS traffic in smart meters considering maximizing a weighted utility measure. Numerical results demonstrate the effectiveness of the proposed model in terms of satisfying latency requirement and efficient bandwidth allocation.