Data Warehouses (DWs) are core components of Business Intelligence (BI). Missing data in DWs have a great impact on data analyses. Therefore, missing data need to be completed. Unlike other existing data imputation methods mainly adapted for facts, we propose a new imputation method for dimensions. This method contains two steps: 1) a hierarchical imputation and 2) a k-nearest neighbors (KNN) based imputation. Our solution has the advantage of taking into account the DW structure and dependency constraints. Experimental assessments validate our method in terms of effectiveness and efficiency.