The novelty of the COVID-19 disease and the speed of spread has created a colossal chaos, impulse among researchers worldwide to exploit all the resources and capabilities to understand and analyze characteristics of the coronavirus in term of the ways it spreads and virus incubation time. For that, the existing medical features like CT and X-ray images are used. For example, CT-scan images can be used for the detection of lung infection. But the challenges of these features such as the quality of the image and infection characteristics limitate the effectiveness of these features. Using artificial intelligence (AI) tools and computer vision algorithms, the accuracy of detection can be more accurate and can help to overcome these issues. This paper proposes a multi-task deep-learning-based method for lung infection segmentation using CT-scan images. Our proposed method starts by segmenting the lung regions that can be infected. Then, segmenting the infections in these regions. Also, to perform a multi-class segmentation the proposed model is trained using the two-stream inputs. The multi-task learning used in this paper allows us to overcome shortage of labeled data. Also, the multi-input stream allows the model to do the learning on many features that can improve the results. To evaluate the proposed method, many features have been used. Also, from the experiments, the proposed method can segment lung infections with a high degree performance even with shortage of data and labeled images. In addition, comparing with the state-of-the-art method our method achieves good performance results.