Traditional clustering algorithms are generally only suitable for static data processing， while the real world data are often large and changeable， so static clustering algorithms cannot provide the analysis and learning of evolution rules for dynamic data. On one hand， the clustering of evolutionary data needs to reflect the reasonable cluster partition of data at each snapshot； on the other hand， it needs to make sure the dynamic clustering results are as smooth as possible. This paper proposes an adaptive time-smoothed evolutionary clustering framework， which takes into account of the unknown relationship between the current data and the historical data. By imposing a time window for backtracking， it adaptively finds the most relevant historical snapshot to the current snapshot. Meanwhile， it fuses the static similarity based on the Itakura-Saito distance and the dynamic similarity based on the time series to compute， so as so compute the similarity matrix on each snapshot. Under this framework， this paper further proposes two adaptive time-smoothed evolutionary spectral clustering algorithms， which define the time cost from different aspects， and obtain different evolutionary clustering results. Experiments on real datasets show that the two proposed algorithms can effectively utilize historical data， and achieve better clustering performance as well as better temporal smoothness.