Due to the diversity and complexity of corona virus disease 2019 (COVID-19), medical imaging plays an increasingly important role. The CT images have good timeliness and positive sensitivity, but the price is relatively expensive. Conversely, X-ray images have the characteristics of fast imaging speed and less radiation damage to the human body. To ensure the authenticity and effectiveness of the proposed network in detecting negative and positive COVID-19, a mixed dataset is created through public X-ray and CT images. To solve the problem of feature similarity between the lung diseases and the COVID-19, the extracted features are enhanced by an adaptive region enhancement algorithm. Besides, the depth network based on the residual blocks and the Dense blocks is trained and tested. The residual blocks effectively improve the accuracy of the model and the non-linear COVID-19 features are obtained by cross-layer link. The Dense blocks effectively improve the robustness of the model by connecting local and abstract information. The sensitivity, specificity, PPV, NPV, AUC, and accuracy can reach 0.99 on the mixed X-ray and CT dataset. The proposed COVID-RDNet model has good negative and positive COVID-19 classification performance, which can assist doctors to judge the infection status of patients.