Click-through rate (CTR) prediction models often depict a user's interest as a fixed-length vector derived from her historical behaviors, encompassing various types of actions such as clicks, likes, and purchases. Recently, several approaches have been developed to capture users' multiple interests. For accurate multi-behavior prediction, it is essential to represent complex behavior dependencies effectively, as these dependencies are manifested through different behavior types. Advanced multi-behavior models learn relationships among behaviors based on all previous interactions. However, diverse behaviors may indicate different user intentions and unrelated interactions can distract from the target behavior that needs to be predicted. In order to address the limitations highlighted before, we propose a new approach called User Intent Profiling Network (UIPN) for modeling multiple behaviors. UIPN is capable of learning behavior-specific and behavior-dependent intention embedding vectors for users' various behaviors using user intent extractors. These extractors can provide explicit explanations of users' interactions in the online advertising system. The proposed approach has been validated by extensive experiments on public datasets, which illustrate its effectiveness.