Future high-resolution short-range automotive radar will have a higher false alarm probability than the conventional low-resolution radar has. In a high-resolution radar, the reception signal becomes sensitive to the difference between intended and unintended objects. However, automotive radars must distinguish targets from background objects that are the same order of size; it leads to an increase in the false alarm probability. In this paper, a CFAR circuit for obtaining the target mean power, as well as the background mean power, is proposed to reduce the false alarm probability for high-resolution radars working in automotive environments. The proposed method is analytically evaluated with use of the characteristic function method. Spatial correlation is also considered in the evaluation, because the sizes of the both target and background objects approach the dimension of several range cells. Result showed the proposed CFAR with use of two alongside range cells could reduce the ratio of 6.4dB for an example of an automotive situation.