The Coronavirus Disease (COVID-19) caused a lot of mortality. The high mortality rate occurred because of the physicians' wrong or late identification of COVID-19 severity. So, developing Computer-Aided Design (CAD) systems using Artificial Intelligence (AI) techniques is critical to help physicians correctly identify the severity of COVID-19 in the early stages of the pandemic and then decrease the COVID-19 mortality percentage. In this paper, we develop a new green CAD system using a new hybrid handcrafted feature extraction algorithm and two-stage neural network architecture to grade the COVID-19 patient based on Computed Tomography (CT) scan images as having a moderate, severe, or critical infection. Because the proposed system uses handcrafted feature extraction algorithms, it consumes minimum resources and time than recent works. The proposed system consists of three phases: lesion segmentation, feature extraction, and diagnosis. Firstly, lesions from the CT scan image are manually segmented, and then three schemes are applied to extract salient features from the segmented lesions. These schemes are the Histogram of Oriented Gradients (HOG), Speeded Up Robust Features (SURF), and a new hybrid method that consists of cascading Discrete Wavelet Transform (DWT) and Gray-Level Co-Occurrence Matrix (GLCM). Then, the Cumulative Distribution Function (CDF) is computed for each scheme to extract the statistical markers. In the grading phase, a two-stage neural network approach is used. First, the extracted features are individually trained and tested for each scheme in the first neural network stage, and then the results of the first stage are combined to train and test each patient in the second neural network stage. The performance of the proposed system was assessed on a CT image dataset of 300 COVID-19-positive patients collected from the Cancer Imaging Archive (TCIA) website. The experimental results showed that our proposed system achieved 100% accuracy and kappa when the dataset was partitioned into 80% for training and 20% for testing. Also, it achieved 95.67% ± 0.47, 99.33% ± 0.77, and 100% ± 0 accuracies and 93.48% ± 0.74, 98.997% ± 1.16, and 100% ± 0 kappa values when the data was organized using 2, 4, and 10 folds, respectively. A green complexity algorithm analysis shows that this proposed system takes O(n) time complexity and 1 h and 20 min to train and test all cases. The performed green complexity analysis shows that the proposed system consumes 117.80 g Carbon Dioxide Equivalent (CO2e), 130.80 Wh, and 0.13 tree months for the carbon footprint, the energy needed, and the carbon sequestration, respectively. These results show that the proposed work consumes fewer resources and provides a green CAD system. • This paper proposes a CAD system for COVID-19 severity prediction. • The proposed system uses a two-stage neural network architecture. • The proposed system consists of two phases: feature extraction and severity identification. • A green complexity analysis is performed to prove the greenness of the proposed system. [ABSTRACT FROM AUTHOR]