In analyzing data from multiple participants, such as the US Census, the privacy of sensitive information should be protected and the analysis needs to be robust against malicious participants injecting corrupted data. To this end, we study a fundamental statistical problem of estimating the covariance from i.i.d. samples of a zero mean Gaussian distribution. We provide the first efficient algorithm that achieves both robustness and privacy. We provide statistical guarantees showing that we pay an extra factor d in the sample complexity, compared to the minimax optimal sample complexity.