Cybersecurity has received significant attention globally, with the ever-continuing expansion of internet usage, due to growing trends and adverse impacts of cybercrimes, which include disrupting businesses, corrupting or altering sensitive data, stealing or exposing information, and illegally accessing a computer network. As a popular way, different kinds of firewalls, antivirus systems, and Intrusion Detection Systems (IDS) have been introduced to protect a network from such attacks. Recently, Machine Learning (ML), including Deep Learning (DL) based autonomous systems, have been state-of-the-art in cyber security, along with their drastic growth and superior performance. This study aims to develop a novel IDS system that gives more attention to classifying attack cases correctly and categorizes attacks into subclass levels by proposing a two-step process with a cascaded framework. The proposed framework recognizes the attacks using one ML model and classifies them into subclass levels using the other ML model in successive operations. The most challenging part is to train both models with unbalanced cases of attacks and non-attacks in the datasets, which is overcome by proposing a data augmentation technique. Precisely, limited attack samples of the dataset are augmented in the training set to learn the attack cases properly. Finally, the proposed framework is implemented with NN, the most popular ML model, and evaluated with the NSL-KDD dataset by conducting a rigorous analysis of each subclass emphasizing the major attack class. The proficiency of the proposed cascaded approach with data augmentation is compared with the other three models: the cascaded model without data augmentation and the standard single NN model with and without the data augmentation technique. Experimental results on the NSL-KDD dataset have revealed the proposed method as an effective IDS system and outperformed existing state-of-the-art ML models.