Electrocardiogram (ECG) monitoring systems are widely used in healthcare. ECG data must be compressed for transmission and storage. Furthermore, there is a need to be able to directly process biomedical signals in encrypted domains to ensure the protection of patients' privacy. Existing encryption-then-compression (ETC) approaches for multimedia using the state-of-the-art encryption techniques inevitably sacrifice the compression efficiency or signal quality. This paper presents the first ETC approach for processing ECG data. The proposed approach not only can protect data privacy but also provide the same quality of the reconstructed signals without sacrificing the compression efficiency relative to unencrypted compressions. Specifically, the singular value decomposition technique is used to compress the data such that the proposed system can provide quality-control compressed data, even though the data has been encrypted. Experimental results prove the proposed system to be an effective technique for assuring data security as well as compression performance for ECG data.