Deep neural networks (DNNs) are widely used in various application domains such as image processing, speech recognition, and natural language processing. However, testing DNN models may be challenging due to the complexity and size of their input domain. Particularly, testing DNN models often requires generating or exploring large unlabeled datasets. In practice, DNN test oracles, which identify the correct outputs for inputs, often require expensive manual effort to label test data, possibly involving multiple experts to ensure labeling correctness. In this paper, we propose DeepGD, a black-box multi-objective test selection approach for DNN models. It reduces the cost of labeling by prioritizing the selection of test inputs with high fault-revealing power from large unlabeled datasets. DeepGD not only selects test inputs with high uncertainty scores to trigger as many mispredicted inputs as possible but also maximizes the probability of revealing distinct faults in the DNN model by selecting diverse mispredicted inputs. The experimental results conducted on four widely used datasets and five DNN models show that in terms of fault-revealing ability: (1) White-box, coverage-based approaches fare poorly, (2) DeepGD outperforms existing black-box test selection approaches in terms of fault detection, and (3) DeepGD also leads to better guidance for DNN model retraining when using selected inputs to augment the training set.