The most important problem in telecommunication is bandwidth limitation due to the uncontrolled growth of wireless technology. Deploying dynamic spectrum access techniques is one of the procedures provided for efficient use of bandwidth. In recent years, cognitive radio network introduced as a tool for efficient use of spectrum. These radios are able to use radio resources by recognizing surroundings via sensors and signal operations that means use these resources only when authorized users do not use their spectrum. Secondary users are unauthorized ones that must avoid from interferences with primary users transmission. Secondary users must leave channel due to preventing damages to primary users whenever these users discretion. In this article, spectrum opportunities prediction based on Recurrent Neural Network for bandwidth optimization and reducing the amount of energy by predicting spectrum holes discovery for quality of services optimization proposed in OFDM-based cognitive radio network based on probability density function. The result of the simulation represent acceptable value of SNR and bandwidth optimization in these networks that allows secondary users to taking spectrum and sending data without collision and overlapping with primary users.