Feature construction and feature selection are two common pre-processing methods for classification. Genetic Programming (GP) can be used to solve feature construction and feature selection tasks due to its flexible representation. In this paper, a filter-based multiple feature construction approach using GP named FCM that stores top individuals is proposed, and a filter-based feature selection approach using GP named FS that uses correlation-based evaluation method is employed. A hybrid feature construction and feature selection approach named FCMFS that first constructs multiple features using FCM then selects effective features using FS is proposed. Experiments on nine datasets show that features selected by FS or constructed by FCM are all effective to improve the classification performance comparing with original features, and our proposed FCMFS can maintain the classification performance with smaller number of features comparing with FCM, and can obtain better classification performance with smaller number of features than FS on the majority of the nine datasets. Compared with another feature construction and feature selection approach named FSFCM that first selects features using FS then constructs features using FCM, FCMFS achieves better performance in terms of classification and the smaller number of features. The comparisons with three state-of-art techniques show that our proposed FCMFS approach can achieve better experimental results in most cases.