Recently, thermal metamaterials have attracted more and more attention, and they have been used to manipulate the flow of heat flux. As a typical case, the thermal cloak can conceal the heat signature of an object. To the best of our knowledge, most of researches on cloak have focused on the case in which the background is a single homogeneous medium. However, cloaking in the layered and gradually changing backgrounds is very common in our real life such as hiding the buried mines in several soil backgrounds. In this paper, on the basis of transformation thermodynamics, a general expression of the thermal conductivity for two-dimensional thermal cloak with arbitrary shape in the layered and gradually changing backgrounds is derived by the coordinate transformation method. According to the expression, we design the thermal cloak in different inhomogeneous backgrounds. Results of full wave simulation show that heat flux can travel around the protection area and eventually return to their original path. The temperature profile inside the thermal cloak keeps unchanged, and the temperature field outside the thermal cloak is not distorted, which proves that the cloak has a thermal protection and thermal stealth function. In the end, we propose a useful method of utilizing homogeneous isotropic materials to construct a thermal device according to the equivalent medium theory. The method is closer to the practical application of the project because of considering the complex backgrounds. At the same time, this technology provides a feasible method to control heat transfer in the future and has great significance for thermal stealth and thermal protection.