Abstract: Differential specific heat measurement detects the difference in specific heat between two samples. The system has an extremely high resolution greater than 10-4, and is suitable for measuring a tiny change in specific heat when a material experiences a phase transition, or for measuring electronic specific heat over a wide temperature range. In this paper, we describe the principle and method of high-resolution continuous heating differential specific heat measurement. In addition, we introduce its application in the studies of electronic specific heat, normal state pseudo-gaps, and superconducting condensed energy in high Tc cuprates.