In this paper, we design the multi-class privacy-preserving cloud computing scheme (MPCC) leveragingcompressive sensing for compact sensor data representation and secrecy for data encryption. Three variantsof the MPCC scheme are proposed, realizing statistical decryption for smart meters, and data anonymizationfor images and electrocardiogram signals. The proposed MPCC variants achieve two-class secrecy, one for thesuperuser who can retrieve the exact sensor data and the other for the semi-authorized user, who can onlyobtain the statistical data such as mean, variance, etc., or the signals without sensitive part of information,depending on which variant of the MPCC is used. MPCC scheme allows computationally expensive sparsesignal recovery to be performed at the cloud without compromising data confidentiality to the cloud serviceproviders. In this way, it mitigates the issues in data transmission energy and storage caused by massive IoTsensor data, as well as the increasing concerns about IoT data privacy in cloud computing. We show that theMPCC scheme has lower computational complexity at the IoT sensor device and data end-users than the state-of-the-art schemes. Experimental results on three datasets, i.e., smart meter, electrocardiogram, and images,demonstrate the MPCC's performance in statistical decryption and data anonymization