Active learning is a useful technique for tasks for which unlabeled data is abundant but manual labeling is expensive. One example of such a task is semantic role labeling (SRL), which relies heavily on labels from trained linguistic experts. One challenge in applying active learning algorithms for SRL is that the complete knowledge of the SRL model is often unavailable, against the common assumption that active learning methods are aware of the details of the underlying models. In this paper, we present an active learning framework for black-box SRL models (i.e., models whose details are unknown). In lieu of a query strategy based on model details, we propose a neural query strategy model that embeds both language and semantic information to automatically learn the query strategy from predictions of an SRL model alone. Our experimental results demonstrate the effectiveness of both this new active learning framework and the neural query strategy model.