In the field of diagnosis and treatment planning of Coronavirus disease 2019 (COVID-19), accurate infected area segmentation is challenging due to the significant variations in the COVID-19 lesion size, shape, and position, boundary ambiguity, as well as complex structure. To bridge these gaps, this study presents a robust deep learning model based on a novel multi-scale contextual information fusion strategy, called Multi-Level Context Attentional Feature Fusion (MLCA2F), which consists of the Multi-Scale Context-Attention Network (MSCA-Net) blocks for segmenting COVID-19 lesions from Computed Tomography (CT) images. Unlike the previous classical deep learning models, the MSCA-Net integrates Multi-Scale Contextual Feature Fusion (MC2F) and Multi-Context Attentional Feature (MCAF) to learn more lesion details and guide the model to estimate the position of the boundary of infected regions, respectively. Practically, extensive experiments are performed on the Kaggle CT dataset to explore the optimal structure of MLCA2F. In comparison with the current state-of-the-art methods, the experiments show that the proposed methodology provides efficient results. Therefore, we can conclude that the MLCA2F framework has the potential to dramatically improve the conventional segmentation methods for assisting clinical decision-making.