Several recent works have studied feature evolvable learning. They usually assume that features would not vanish or appear in an arbitrary way; instead, old features vanish and new features emerge as the hardware device collecting the data features is replaced. However, the existing learning algorithms for feature evolution only utilize the first-order information of data streams and ignore the second-order information which can reveal the correlations between features and thus significantly improve the classification performance. We propose a Confidence-Weighted learning for Feature Evolution (CWFE) algorithm to solve the aforementioned problem. First, second-order confidence-weighted learning is introduced to update the prediction model. Next, to make full use of the learned model, a linear mapping is learned in the overlapping period to recover the old features. Then, the existing model is updated with the recovered old features and, at the same time, a new prediction model is learned with the new features. Furthermore, two ensemble methods are introduced to utilize the two models. Finally, experimental studies show that the proposed algorithms outperform existing feature evolvable learning algorithms.