This paper describes a neural network scheduler for scheduling independent and nonpreemptable tasks with deadlines and resource requirements in critical real-time applications, in which a schedule is to be obtained within a short time span. The proposed neural network scheduler is an integrate model of two Hopfield-Tank neural network models. To cope with deadlines, a heuristic policy which is modified from the earliest deadline policy is embodied into the proposed model. Computer simulations show that the proposed neural network scheduler has a promising performance, with regard to the probability of generating a feasible schedule, compared with a scheduler that executes a conventional algorithm performing the earliest deadline policy.