A face detection in color images is important for many multimedia applications. It is first step for face recognition and can be used for classifying specific shorts. This paper describes a new method to detect faces in color images based on the skin color and hair color. This paper presents a fuzzy-based method for classifying skin color region in a complex background under varying illumination. The Fuzzy rule bases of the fuzzy system are generated using training method like a genetic algorithm(GA). We find the skin color region and hair color region using the fuzzy system and apply the convex-hull to each region and find the face from their intersection relationship. To validity the effectiveness of the proposed method, we make experiment with various cases.