Taxi demand forecasting is crucial to building an efficient transportation system in a smart city. Accurate taxi demand forecasting could help the taxi management platform to allocate taxi resources in advance, alleviate traffic congestion, and reduce passenger waiting time. Thus, more efforts in industrial and academic circles have been directed towards the cities' taxi service demand prediction (CTSDP). However, the complex nonlinear spatio-temporal relationship in demand data makes it challenging to construct an accurate forecasting model. There remain challenges in perceiving the micro spatial characteristics and the macro periodicity characteristics from cities' taxi service demand data. What's more, the existing methods are significantly insufficient for exploring the potential multi-time patterns from these demand data. To meet the above challenges, and also stimulated by the human perception mechanism, we propose a Multi-Sensory Stimulus Attention (MSSA) model for CTSDP. Specifically, the MSSA model integrates a detail perception attention and a stimulus variety attention for capturing the micro and macro characteristics from massive historical demand data, respectively. The multiple time resolution modules are employed to capture multiple potential spatio-temporal periodic features from massive historical demand data. Extensive experiments on the yellow taxi trip records data in Manhattan show that the MSSA model outperforms the state-of-the-art baselines.