Websites can increase their security and prevent harmful Internet attacks by providing CAPTCHA verification for determining whether end-user is a human or a robot. Text-based CAPTCHA is the most common and designed to be easily recognized by humans and difficult to identify by machines or robots. However, with the dramatic advancements in deep learning, it becomes much easier to build convolutional neural network (CNN) models that can efficiently recognize text-based CAPTCHAs. In this study, we introduce an efficient CNN model that uses attached binary images to recognize CAPTCHAs. By making a specific number of copies of the input CAPTCHA image equal to the number of characters in that input CAPTCHA image and attaching distinct binary images to each copy, we build a new CNN model that can recognize CAPTCHAs effectively. The model has a simple structure and small storage size and does not require the segmentation of CAPTCHAs into individual characters. After training and testing the proposed CAPTCHA recognition CNN model, the achieved experimental results reveal the strength of the model in CAPTCHA character recognition.