Currently, we witness the severe spread of the pandemic of the new Corona virus, COVID-19, which causes dangerous symptoms to humans and animals, its complications may lead to death. Although convolutional neural networks (CNNs) is considered the current state-of-the-art image classification technique, it needs massive computational cost for deployment and training. In this paper, we propose an improved hybrid classification approach for COVID-19 images by combining the strengths of CNNs (using a powerful architecture called Inception) to extract features and a swarm-based feature selection algorithm (Marine Predators Algorithm) to select the most relevant features. A combination of fractional-order and marine predators algorithm (FO-MPA) is considered an integration among a robust tool in mathematics named fractional-order calculus (FO). The proposed approach was evaluated on two public COVID-19 X-ray datasets which achieves both high performance and reduction of computational complexity. The two datasets consist of X-ray COVID-19 images by international Cardiothoracic radiologist, researchers and others published on Kaggle. The proposed approach selected successfully 130 and 86 out of 51 K features extracted by inception from dataset 1 and dataset 2, while improving classification accuracy at the same time. The results are the best achieved on these datasets when compared to a set of recent feature selection algorithms. By achieving 98.7%, 98.2% and 99.6%, 99% of classification accuracy and F-Score for dataset 1 and dataset 2, respectively, the proposed approach outperforms several CNNs and all recent works on COVID-19 images. © 2020, The Author(s).