In this paper, we propose a new method for online learning in varying feature spaces (VFS) where the feature space of instances continually evolves. The proposed method, termed Online Imputation-based Learning (OIL), first imputes missing values and subsequently trains a classifier within a complete feature space. A significant advantage of this approach is the potential for considerable improvements by leveraging well-established research in both imputation and classification techniques. Furthermore, it offers the flexibility to easily modify model configurations based on specific conditions. The experimental results demonstrate that OIL not only performs comparably or even better than the state-of-the-art rival method in regularly varying data streams but also in arbitrarily varying data streams. This is evidenced across 13 benchmark datasets. Following this, we perform an ablation study under diverse conditions to further investigate the efficacy and robustness of various OIL configurations.