In this paper, we study sleeping and power control of a single-cell cellular network with bursty traffic. The base station (BS) sleeps whenever the system is empty, and wakes up when N users are assembled. The service capacity of the BS in the active mode is controlled through its transmitting power. The total power consumption and average delay for bursty traffic that follows the Interrupted Poisson Process (IPP) are analyzed. We discuss when the BS should sleep and the impact of traffic burstiness on it. The impact of the sleeping threshold and the transmitting power on the system performance is also investigated. The numerical results show that given the average traffic load, the more bursty the traffic is, the less the total power is consumed, while the delay performance of the more bursty traffic is better only under certain circumstances.