The level of ripeness is essential in determining the quality of bananas. To correctly estimate banana maturity, the metrics of international marketing standards need to be considered. However, the process of assessing the maturity of bananas at an industrial level is still carried out using manual methods. The use of CNN models is an attractive tool to solve the problem, but there is a limitation regarding the availability of sufficient data to train these models reliably. On the other hand, in the state-of-the-art, existing CNN models and the available data have reported that the accuracy results are acceptable in identifying banana maturity. For this reason, this work presents the generation of a robust dataset that combines real and synthetic data for different levels of banana ripeness. In addition, it proposes a simple CNN architecture, which is trained with synthetic data and using the transfer learning technique, the model is improved to classify real data, managing to determine the level of maturity of the banana. The proposed CNN model is evaluated with several architectures, then hyper-parameter configurations are varied, and optimizers are used. The results show that the proposed CNN model reaches a high accuracy of 0.917 and a fast execution time.