A clinically meaningful distance metric, which is learned from measuring patient similarity, plays an important role in clinical decision support applications. Several metric learning approaches have been proposed to measure patient similarity, but they are mostly designed for learning the metric at only one time point/interval. It leads to a problem that those approaches cannot reflect the similarity variations among patients with the progression of diseases. In order to capture similarity information from multiple future time points simultaneously, we formulate a multi-task metric learning approach to identify patient similarity. However, it is challenging to directly apply traditional multi-task metric learning methods to learn such similarities due to the high dimensional, complex and noisy nature of healthcare data. Besides, the disease labels often have clinical relationships, which should not be treated as independent. Unfortunately, traditional formulation of the loss function ignores the degree of labels' similarity. To tackle the aforementioned challenges, we propose mtTSML, a multi-task triplet constrained sparse metric learning method, to monitor the similarity progression of patient pairs. In the proposed model, the distance for each task can be regarded as the combination of a common part and a task-specific one in the transformed low-rank space. We then perform sparse feature selection for each individual task to select the most discriminative information. Moreover, we use triplet constraints to guarantee the margin between similar and less similar pairs according to the ordered information of disease severity levels (i.e. labels). The experimental results on two real-world healthcare datasets show that the proposed multi-task metric learning method significantly outperforms the state-of-the-art baselines, including both single-task and multi-task metric learning methods.