Standard approaches for variable selection in linear models are not tailored to deal properly with high-dimensional and incomplete data. Currently, methods dedicated to high-dimensional data handle missing values by ad hoc strategies, like complete case analysis or single imputation, while methods dedicated to missing values, mainly based on multiple imputation, do not discuss the imputation method to use with high-dimensional data. Consequently, both approaches appear to be limited for many modern applications. With inspiration from ensemble methods, a new variable selection method is proposed. It extends classical variable selection methods in the case of high-dimensional data with or without missing data. Theoretical properties are studied and the practical interest is demonstrated through a simulation study, as well as through an application to models specification in sequential multiple imputation. In the low-dimensional case, the procedure improves the control of the error risks, especially type I error, even without missing values for stepwise, lasso or knockoff methods. With missing values, the method performs better than reference selection methods based on multiple imputation. Similar performances are obtained in the high-dimensional case with or without missing values.