Nowadays, with the emergence of software-defined networking, sketch-based network measurements have been widely used to balance the tradeoff between efficiency and reliability. The simplicity and generality of a sketch-based system allow it to track divergent performance metrics and deal with heterogeneous traffic characteristics. However, most of the existing proposals mainly consider priority-agnostic measurements, which introduce equal error probability to different classes of traffic. While network measurements are usually task-oriented, e.g., traffic engineering or intrusion detection, a system operator may be interested only in tracking specific types of traffic and expect various levels of tracking resolutions for different traffic classes. To achieve this goal, we propose MC-Sketch (Multi-Class Sketch), a priority-aware system that provides various classes of traffic with differential accuracy subject to the limited resources of a programmable switch. It privileges higher priority traffic in accessing the sketch over background traffic and naturally provides heterogeneous tracking resolutions. The experimental results and large-scale analysis show that MC-Sketch reduces the measurement errors of high priority flows by 56.92% without harming the overall accuracy much.