A BGK model on the 2D adaptive unstructured mesh is developed within a finite volume framework, which consists of two steps:the solution reconstruction step and the gas evolution step. The computation domain is tessellated with triangular elements. In the reconstruction step, a high-order ENO scheme based on the least-square principle is employed to obtain the derivatives. In the gas evolution step, with the axis rotation, the flux through each side of the triangular element is obtained. Some test cases validate the capability of the current numerical approach to provide a highly accurate solution in complex geometries. It is observed that the BGK model provides a reasonable alternative to Riemann solvers.