Fiber of optical lens and color industrial video camera are used to capture image of cutting point in laser cutting process. Blue channel, green channel and red channel images are adopted to analyze cutting point geometry shape from color image. The position of laser beam focal point is used as origin of coordinates and the coordinate system is set up. The x axis is original direction and interval is 45 degree, the edge points of laser cutting region are searched from eight directions. According to distances from origin of coordinates to edge points, the laser cutting direction and cutting peak are fixed. Parabola model is set up, and the objective function is designed according to gray feature, gradient feature and direction feature, and the objective function is used to identify edge at bilateral cutting peak, and then cutting point geometry shape is identified. Test shows that the method has preferable adaptability, accuracy and real-time quality.