Cybersecurity practitioners generate a Completely Automated Public Turing test to tell Computers and Humans Apart (CAPTCHAs) as a form of security mechanism in website applications, in order to differentiate between human end-users and machine bots. They tend to use standard security to implement CAPTCHAs in order to prevent hackers from writing malicious automated programs to make false website registrations and to restrict them from stealing end-users’ private information. Among the categories of CAPTCHAs, the text-based CAPTCHA is the most widely used. However, with the evolution of deep learning, it has been so dramatic that tasks previously thought not easily addressable by computers and used as CAPTCHA to prevent spam are now possible to break. The workflow of CAPTCHA breaking is a combination of efforts, approaches, and the development of the computation-efficient Convolutional Neural Network (CNN) model that attempts to increase accuracy. In this study, in contrast to breaking the whole CAPTCHA images simultaneously, this study split four-character CAPTCHA images for the individual characters with a 2-pixel margin around the edges of a new training dataset, and then proposed an efficient and accurate Depth-wise Separable Convolutional Neural Network for breaking text-based CAPTCHAs. Most importantly, to the best of our knowledge, this is the first CAPTCHA breaking study to use the Depth-wise Separable Convolution layer to build an efficient CNN model to break text-based CAPTCHAs. We have evaluated and compared the performance of our proposed model to that of fine-tuning other popular CNN image recognition architectures on the generated CAPTCHA image dataset. In real-time, our proposed model used less time to break the text-based CAPTCHAs with an accuracy of more than 99% on the testing dataset. We observed that our proposed CNN model has efficiently improved the CAPTCHA breaking accuracy and streamlined the structure of the CAPTCHA breaking network as compared to other CAPTCHA breaking techniques.