Test suites play a key role in ensuring software quality. A good test suite may detect more faults than a poor-quality one. Mutation testing is a powerful methodology for evaluating the fault-detection ability of test suites. In mutation testing, a large number of mutants may be generated and need to be executed against the test suite under evaluation to check how many mutants the test suite is able to detect, as well as the kind of mutants that the current test suite fails to detect. Consequently, although highly effective, mutation testing is widely recognized to be also computationally expensive, inhibiting wider uptake. To alleviate this efficiency concern, we propose Predictive Mutation Testing (PMT): the first approach to predicting mutation testing results without executing mutants. In particular, PMT constructs a classification model, based on a series of features related to mutants and tests, and uses the model to predict whether a mutant would be killed or remain alive without executing it. PMT has been evaluated on 163 real-world projects under two application scenarios (cross-version and cross-project). The experimental results demonstrate that PMT improves the efficiency of mutation testing by up to 151.4X while incurring only a small accuracy loss. It achieves above 0.80 AUC values for the majority of projects, indicating a good tradeoff between the efficiency and effectiveness of predictive mutation testing. Also, PMT is shown to perform well on different tools and tests, be robust in the presence of imbalanced data, and have high predictability (over 60% confidence) when predicting the execution results of the majority of mutants.