Video question answering (VideoQA) is challenging given its multimodal combination of visual understanding and natural language understanding. While existing approaches seldom leverage the appearance-motion information in the video at multiple temporal scales, the interaction between the question and the visual information for textual semantics extraction is frequently ignored. Targeting these issues, this paper proposes a novel Temporal Pyramid Transformer (TPT) model with multimodal interaction for VideoQA. The TPT model comprises two modules, namely Question-specific Transformer (QT) and Visual Inference (VI). Given the temporal pyramid constructed from a video, QT builds the question semantics from the coarse-to-fine multimodal co-occurrence between each word and the visual content. Under the guidance of such question-specific semantics, VI infers the visual clues from the local-to-global multi-level interactions between the question and the video. Within each module, we introduce a multimodal attention mechanism to aid the extraction of question-video interactions, with residual connections adopted for the information passing across different levels. Through extensive experiments on three VideoQA datasets, we demonstrate better performances of the proposed method in comparison with the state-of-the-arts.