Electromyogram (EMG) based human computer interface (HCI) is an attractive technique to monitor a patient, control an artificial arm, or play a game. Since EMG processing requires high sampling and transmission rates, a compression technique is important to implement an ultra-low power wireless EMG system. Previous study has a limitation due to the complexity of algorithm and the non-sparsity nature of EMG. In this study, we proposed a new EMG compression scheme based on a compressive covariance sensing (CCS). The covariance recovered from compressed EMG was used to classify user's gestures. The proposed method was verified with NinaPro open source data, which contains 49 gestures with 6 times repetition. As a result, the proposed CCS based EMG compression technique showed good covariance recovery performance and high classification rate as well as superior compression rate.