In deadline scheduling, jobs have deadlines by which they are completed. The scheduling algorithm determines which jobs are executed at each time. Then only the completed jobs contribute to the throughput or gain of the algorithm. The jobs have arbitrary weights and the gain of the algorithm is given as the sum of weights of the completed jobs. The goal of the scheduling algorithm is to maximize its gain. In this paper, we consider online non-preemptive scheduling, where jobs arrive online and the scheduling algorithm has no information about jobs arriving ahead. Also the jobs cannot be preempted or rejected while they are executed. For this problem, we obtain lower bounds for any online algorithms and also we propose an optimal online algorithm meeting the lower bounds.