In today's Internet of Things research community, Cloud-fog framework is a potential technology for Internet of Things to support energy consumption of an IoT system and delay-sensitive applications that require almost real-time responses. However, how to schedule the computational tasks which is to offload to fog nodes or cloud nodes is not fully addressed until now. In this paper, in order to solve the complex task scheduling problem with some priority constraints of IoT applications taking into account the energy consumption and reducing energy consumption on the condition of satisfying the mix deadline, we formulate an associated task scheduling problem into a constrained optimization problem in cloud-fog environment. A laxity and ant colony system algorithm(LBP-ACS) is put forward to tackle this problem. In this algorithm, a strategy of task scheduling is not only considering the priority of a task, but also its finished deadline. In order to handle the sensitivity of task delay, the laxity-based priority algorithm is adopted to construct a task scheduling sequence with reasonable priority. Meanwhile, to minimize the total energy consumption, the constrained optimization algorithm based on ant colony system algorithm is used to obtain the approximate optimal scheduling scheme in the global. Compared with other algorithms, the experimental results show that the proposed algorithm can effectively reduce the energy consumption of processing all tasks, while ensuring reasonable scheduling length and reducing the failure rate of associated tasks scheduling with mixed deadlines.