Deep Neural Network (DNN) models are widely used for image classification. While they offer high performance in terms of accuracy, researchers are concerned about if these models inappropriately make inferences using features irrelevant to the target object in a given image. To address this concern, we propose a metamorphic testing approach that assesses if a given inference is made based on irrelevant features. Specifically, we propose two metamorphic relations (MRs) to detect such unreliable inferences. These relations expect (a) the classification results with different labels or the same labels but less certainty from models after corrupting the relevant features of images, and (b) the classification results with the same labels after corrupting irrelevant features. The inferences that violate the metamorphic relations are regarded as unreliable inferences. Our evaluation demonstrated that our approach can effectively identify unreliable inferences for single-label classification models with an average precision of 64.1% and 96.4% for the two MRs, respectively. As for multi-label classification models, the corresponding precision for MR-1 and MR-2 is 78.2% and 86.5%, respectively. Further, we conducted an empirical study to understand the problem of unreliable inferences in practice. Specifically, we applied our approach to 18 pre-trained single-label image classification models and 3 multi-label classification models, and then examined their inferences on the ImageNet and COCO datasets. We found that unreliable inferences are pervasive. Specifically, for each model, more than thousands of correct classifications are actually made using irrelevant features. Next, we investigated the effect of such pervasive unreliable inferences, and found that they can cause significant degradation of a model’s overall accuracy. After including these unreliable inferences from the test set, the model’s accuracy can be significantly changed. Therefore, we recommend that developers should pay more attention to these unreliable inferences during the model evaluations. We also explored the correlation between model accuracy and the size of unreliable inferences. We found the inferences of the input with smaller objects are easier to be unreliable. Lastly, we found that the current model training methodologies can guide the models to learn object-relevant features to certain extent, but may not necessarily prevent the model from making unreliable inferences. We encourage the community to propose more effective training methodologies to address this issue.