Depression is a mental disorder that threatens the health and normal life of people. Hence, it is essential to provide an effective way to detect depression. However, research on depression detection mainly focuses on utilizing different parallel features from audio, video, and text for performance enhancement regardless of making full usage of the inherent information from speech. To focus on more emotionally salient regions of depression speech, in this research, we propose a multi-head time-dimension attention-based long short-term memory (LSTM) model. We first extract frame-level features to store the original temporal relationship of a speech sequence and then analyze their difference between speeches of depression and those of health status. Then, we study the performance of various features and use a modified feature set as the input of the LSTM layer. Instead of using the output of the traditional LSTM, multi-head time-dimension attention is employed to obtain more key time information related to depression detection by projecting the output into different subspaces. The experimental results show the proposed model leads to improvements of 2.3 and 10.3% over the LSTM model on the Distress Analysis Interview Corpus-Wizard of Oz (DAIC-WOZ) and the Multi-modal Open Dataset for Mental-disorder Analysis (MODMA) corpus, respectively.