A deadline-aware scheduling scheme for the λ grid system is proposed to support a huge computer grid system based on an advanced photonic network technology. The assignment of wavelengths to jobs in order to efficiently carry various services is critical in λ grid networks. Such services have different requirements such as the job completion deadlines and wavelength assignment must consider the job deadlines. The conventional job scheduling approach assigns a lot of time-slots to a call within a short period in order to finish the job as quickly as possible. This raises the blocking probability of short deadline calls. Our proposal assigns wavelengths in A grid networks so as to meet QoS (Quality of Service) guarantees. The proposed scheme assigns time-slots to a call over time according to its deadline, which allows it to increase the system performance in handling short deadline calls, for example, lowering their blocking probability. Computer simulations show that the proposed scheme can reduce the blocking probability by a factor of 100 compared with the conventional scheme under the low load condition in which the ratio of long deadline calls is high. The proposed scheduling scheme can realize more efficient A grid networks.