Objective. Epidermal growth factor receptor (EGFR) mutation genotyping plays a pivotal role in targeted therapy for non-small cell lung cancer (NSCLC). We aimed to develop a computed tomography (CT) image-based hybrid deep radiomics model to predict EGFR mutation status in NSCLC and investigate the correlations between deep image and quantitative radiomics features. Approach. First, we retrospectively enrolled 818 patients from our centre and 131 patients from The Cancer Imaging Archive database to establish a training cohort (N = 654), an independent internal validation cohort (N = 164) and an external validation cohort (N = 131). Second, to predict EGFR mutation status, we developed three CT image-based models, namely, a multi-task deep neural network (DNN), a radiomics model and a feature fusion model. Third, we proposed a hybrid loss function to train the DNN model. Finally, to evaluate the model performance, we computed the areas under the receiver operating characteristic curves (AUCs) and decision curve analysis curves of the models. Main results. For the two validation cohorts, the feature fusion model achieved AUC values of 0.86 ± 0.03 and 0.80 ± 0.05, which were significantly higher than those of the single-task DNN and radiomics models (all P < 0.05). There was no significant difference between the feature fusion and the multi-task DNN models (P > 0.8). The binary prediction scores showed excellent prognostic value in predicting disease-free survival (P = 0.02) and overall survival (P < 0.005) for validation cohort 2. Significance. The results demonstrate that (1) the feature fusion and multi-task DNN models achieve significantly higher performance than that of the conventional radiomics and single-task DNN models, (2) the feature fusion model can decode the imaging phenotypes representing NSCLC heterogeneity related to both EGFR mutation and patient NSCLC prognosis, and (3) high correlations exist between some deep image and radiomics features.