A novel multiple-instance hidden Markov model (MI-HMM) is introduced for classification of time-series data, and its training is developed using stochastic expectation maximization. The MI-HMM provides a single statistical form to learn the parameters of an HMM in a multiple-instance learning framework without introducing any additional parameters. The efficacy of the model is shown both on synthetic data and on a real landmine data set. Experiments on both the synthetic data and the landmine data set show that an MI-HMM can achieve statistically significant performance gains when compared with the best existing HMM for the landmine detection problem, eliminate the ad hoc approaches in training set selection, and introduce a principled way to work with ambiguous time-series data.