Aiming at the problem that the machine learning classification algorithms have insufficient ability to identify minority samples in the imbalanced data classification problems, an imbalanced data classification method L-CCSmote (Least absolute shrinkage and selection operator Constructive Covering Synthetic minority oversampling technique) was proposed by taking the telecom customer churn scenario as an example. Firstly, the churn costumer related features were extracted through Lasso (Least absolute shrinkage and selection operator) to optimize the model input. Then, a neural network was built through Constructive Covering Algorithm (CCA) to generate coverages that conformed to the overall distribution of samples. Finally, a single-sample coverage strategy, a sample diversity strategy and a sample density peak strategy were further proposed to perform a hybrid sampling to balance the data. Total of 13 imbalanced datasets and 2 desensitized telecom customer datasets were selected from KEEL data base, and the proposed method was verified on Logistic Regression (LR) and Support Vector Machine (SVM) classification algorithms respectively. On LR classification algorithm, compared with the Synthetic Minority Oversampling TEchnique Edited nearest neighbor (SMOTE-Enn), the proposed method had the average Geometric MEAN (G-MEAN) increased by 2.32%. On SVM classification algorithm, compared with the Borderline-SMOTE (Borderline Synthetic Minority Oversampling Technique), the proposed method had the average G-MEAN increased by 2.44%. Experimental results show that the proposed method can solve the influence of class skew distribution on classification, and its recognition ability for rare classes is better than that of the classical balanced data classification methods.