This paper focuses on temporal retrieval of activities in videos via sentence queries. Given a sentence query describing an activity, temporal moment retrieval aims at localizing the temporal segment within the video that best describes the textual query. This is a general yet challenging task as it requires the comprehending of both video and language. Existing research predominantly employ coarse frame-level features as the visual representation, obfuscating the specific details (e.g., the desired objects “girl”, “cup” and action “pour”) within the video which may provide critical cues for localizing the desired moment. In this paper, we propose a novel Spatial and Language-Temporal Tensor Fusion (SLTF) approach to resolve those issues. Specifically, the SLTF method first takes advantage of object-level local features and attends to the most relevant local features (e.g., the local features “girl”, “cup”) by spatial attention. Then we encode the sequence of the local features on consecutive frames by employing LSTM network, which can capture the motion information and interactions among these objects (e.g., the interaction “pour” involving these two objects). Meanwhile, language-temporal attention is utilized to emphasize the keywords based on moment context information. Thereafter, a tensor fusion network learns both the intra-modality and inter-modality dynamics, which can enhance the learning of moment-query representation. Therefore, our proposed two attention sub-networks can adaptively recognize the most relevant objects and interactions in the video, and simultaneously highlight the keywords in the query for retrieving the desired moment. Experimental results on three public benchmark datasets (obtained from TACOS, Charades-STA, and DiDeMo) show that the SLTF model significantly outperforms current state-of-the-art approaches, and demonstrate the benefits produced by new technologies incorporated into SLTF.