The Purple Mountain Observatory and the Department of Astronomy, Nanjing University, in Nanjing China-Research, cooperating with the Albert Einstein institute, in Hannover, Germany, put forward a model of the planar co-orbital circular restricted three-body problem, gave the equations of motion, a set of approximation formulas, and an approximate semi-analytical solution. The study is reported in Issue 53, No. 1 of SCIENCE CHINA Physics, Mechanics & Astronomy because of its significant research value.