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A major challenge when trying to detect fraud is that the fraudulent activities form a minority class which make up a very small proportion of the data set. In most data sets, fraud occurs in typically less than 0.5% of the cases. Detecting fraud in such a highly imbalanced data set typically leads to predictions that favor the majority group, causing fraud to remain undetected. We discuss some popular oversampling techniques that solve the problem of imbalanced data by creating synthetic samples that mimic the minority class. A frequent problem when analyzing real data is the presence of anomalies or outliers. When such atypical observations are present in the data, most oversampling techniques are prone to create synthetic samples that distort the detection algorithm and spoil the resulting analysis. A useful tool for anomaly detection is robust statistics, which aims to find the outliers by first fitting the majority of the data and then flagging data observations that deviate from it. In this paper, we present a robust version of ROSE, called robROSE, which combines several promising approaches to cope simultaneously with the problem of imbalanced data and the presence of outliers. The proposed method achieves to enhance the presence of the fraud cases while ignoring anomalies. The good performance of our new sampling technique is illustrated on simulated and real data sets and it is shown that robROSE can provide better insight in the structure of the data. The source code of the robROSE algorithm is made freely available.