Currently used lung disease screening tools are expensive in terms of money and time. Therefore, chest radiograph images (CRIs) are employed for prompt and accurate COVID-19 identification. Recently, many researchers have applied Deep learning (DL) based models to detect COVID-19 automatically. However, their model could have been more computationally expensive and less robust, i.e., its performance degrades when evaluated on other datasets. This study proposes a trustworthy, robust, and lightweight network (ChestCovidNet) that can detect COVID-19 by examining various CRIs datasets. The ChestCovidNet model has only 11 learned layers, eight convolutional (Conv) layers, and three fully connected (FC) layers. The framework employs both the Conv and group Conv layers, Leaky Relu activation function, shufflenet unit, Conv kernels of 3×3 and 1×1 to extract features at different scales, and two normalization procedures that are cross-channel normalization and batch normalization. We used 9013 CRIs for training whereas 3863 CRIs for testing the proposed ChestCovidNet approach. Furthermore, we compared the classification results of the proposed framework with hybrid methods in which we employed DL frameworks for feature extraction and support vector machines (SVM) for classification. The study's findings demonstrated that the embedded low-power ChestCovidNet model worked well and achieved a classification accuracy of 98.12% and recall, F1-score, and precision of 95.75%.