Emotion recognition is a critical component of affective computing. Training accurate machine learning models for emotion recognition typically requires a large amount of labeled data. Due to the subtleness and complexity of emotions, multiple evaluators are usually needed for each affective sample to obtain its ground-truth label, which is expensive. To save the labeling cost, this paper proposes an inconsistency-based active learning approach for cross-task transfer between emotion classification and estimation. Affective norms are utilized as prior knowledge to connect the label spaces of categorical and dimensional emotions. Then, the prediction inconsistency on the two tasks for the unlabeled samples is used to guide sample selection in active learning for the target task. Experiments on within-corpus and cross-corpus transfers demonstrated that cross-task inconsistency could be a very valuable metric in active learning. To our knowledge, this is the first work that utilizes prior knowledge on affective norms and data in a different task to facilitate active learning for a new task, even the two tasks are from different datasets.