In the paper, we propose an adaptive data-driven model-based approach for filling the gaps in time series. The approach is based on the automated evolutionary identification of the optimal structure for a composite data-driven model. It allows adapting the model for the effective gap-filling in a specific dataset without the involvement of the data scientist. As a case study, both synthetic and real datasets from different fields (environmental, economic, etc) are used. The experiments confirm that the proposed approach allows achieving the higher quality of the gap restoration and improve the effectiveness of forecasting models.