Polar Cosine Transform (PCT) is one of the Polar Harmonic Transforms that those kernels are basic waves and harmonic in nature. They are proposed to represent invariant patterns for two dimensional image description and are demonstrated to show superiorities comparing with other methods on extracting rotation invariant patterns for images. However in order to increase the computation speed, fast algorithm for PCT is proposed for real world applications like limited computing environments, large image databases and realtime systems. Based on our previous work, this paper novelly employs relative prime number theory to develop Fast Polar Cosine Transform (FPCT). The proposed FPCT is averagely over 11 ∼ 12.5 times faster than PCT that significantly boost computation process. The experimental results are given to illustrate the effectiveness of the proposed method.