Panel data regression models are commonly used in various fields like medicine and economics. However, using the usual method to estimate these models can lead to inaccurate results when outliers are present. A new robust estimation method has been developed to address this issue. This method performs better than traditional approaches when outliers are present, and it gives similar results to the usual method when outliers are not a factor. This new method has been tested with simulated data and a real-world blood pressure dataset, showing its effectiveness in improving the accuracy of estimates in panel data models.