Action anticipation aims to infer the action in the unobserved segment (future segment) with the observed segment (past segment). Existing methods focus on learning key past semantics to predict the future, but they do not model the temporal continuity between the past and the future. However, past actions are always highly uncertain in anticipating the unobserved future. The absence of temporal continuity smoothing in the video's past-and-future segments may result in an inconsistent anticipation of future action. In this work, we aim to smooth the global semantics changes in the past and future segments. We propose a Consistency-guided Probabilistic Model (CPM), which focuses on learning the globally temporal probabilistic consistency to inhibit the unexpected temporal consistency. The CPM is deployed on the Transformer architecture, which includes three modules of future semantics estimation, global semantics estimation, and global distribution estimation involving the learning of past-to-future semantics, past-and-future semantics, and semantically probabilistic distributions. To achieve the smoothness of temporal continuity, we follow the principle of variational analysis and describe two probabilistic distributions, i.e., a past-aware distribution and a global-aware distribution, which help to estimate the evidence lower bound of future anticipation. In this study, we maximize the evidence lower bound of future semantics by reducing the distribution distance between the above two distributions for model optimization. Extensive experiments demonstrate that the effectiveness of our method and the CPM achieves state-of-the-art performance on Epic-Kitchen100, Epic-Kitchen55, and EGTEA-GAZE.