Multistep traffic speed prediction plays a crucial role in alleviating road congestion and improving transport efficiency. In actual traffic networks, the spatio-temporal dependence among roads dynamically changes over time due to factors such as road conditions and unforeseen incidents, which brings great challenges to multistep traffic speed prediction. Additionally, multistep traffic speed prediction commonly faces the problem of error accumulation, resulting in a loss of prediction accuracy. To address these issues, we propose a Sequence-to-Sequence Spatio-Temporal Attention model (STSSTA) for multistep traffic speed prediction. Specifically, we build an adaptive tuning module to select road preferences and automatically obtain global information about the roads. Then we construct a Sequence-to-Sequence architecture for spatio-temporal feature learning and multistep traffic speed prediction. In particular, in the encoder, we design a Diffusion Graph Convolutional Network (DGCN) and combine it with a Gated Recurrent Unit (GRU) to effectively capture the complex spatio-temporal features within the traffic networks. In the decoder, we introduce a Recalling attention mechanism to alleviate the problem of local information loss caused by encoder compression, thereby reducing error accumulation in multistep prediction. Experiments on METR-LA and PeMS-BAY datasets demonstrate that STSSTA outperforms the baseline models in long-term prediction.