With the development of new communication technologies, the amount of data transmission has increased gradually. To satisfy this increasing computing resource demand effectively, the number of data center networks (DCNs), which are structures composed of servers connected with well-organized-switches, has increased worldwide. However, traditional switches do not efficiently satisfy the needs of DCNs. In recent years, an emerging networking architecture software-defined network (SDN) has been proposed to manage the DCNs to control network switches and to deploy new network protocols. However, the main challenge in DCNs is to balance the load among servers. One potential solution for this challenge is to use machine learning (ML) techniques to tackle network transmission demand. A recent successful ML technique is deep learning (DL) which makes prediction, classification, and decisions by handling large amounts of data. Although DL has drawn increasing attention in many research fields, its applications to networking problems are scarce. In this paper, a DL technique is proposed for the load-balancing of SDN-based DCNs. To train the DL network, the variable load values among links are used. The response time for load balancing of the DL technique is compared with those of different ML algorithms, such as an artificial neural network (ANN), support vector machine (SVM), and logistic regression (LR). The experimental results reveal that the response-time results of ANN and DL are lower than those of the SVM and LR algorithms. Also, DL accuracy is higher than ANN accuracy. As a result, DL is very efficient for the load balancing of SDN-based DCNs.