Energy-efficient scheduling problem in wireless communication system is investigated in this paper. We propose two near-optimal schedulers which have simple structures for the general hard delay constraint scenario. Both single-user and multiuser cases are considered. The first scheduler invokes Gaussian approximation while the second one is inspired by the inverse water-filling (IWF) approach. The scheduling policies consist of a channel-awareness term and a delay-awareness term. Numerical results show that the proposed policies achieve near optimal performance when the total required transmit bits, R, is large. For the multiuser scenario, our scheduling strategy consists of an initial resource (number of time slots) allocation and a slot-by-slot user selection and bit loading algorithm. The former depends on the rate requirement and a priori knowledge of user-dependent channel statistic while the latter use an order statistic based approach designed to minimize the expected total energy consumption.