A snake robot has to raise its head to acquire a wide visual space for planning complex tasks such as inspecting unknown environments, tracking a flying object and acting as a manipulator with its raising part. However, only a few researchers currently focus on analyzing the head-raising motion of snake robots. Thus, a predefined spiral curve method is proposed for the head-raising motion of such robots. First, the expression of the predefined spiral curve is designed. Second, with the curve and a line segments model of a snake robot, a shape-fitting algorithm is developed for constraining the robot's macro shape. Third, the coordinate system of the line segments model of the robot is established. Then, phase-shifting and angle-solving algorithms are developed to obtain the angle sequences of roll, pitch, and yaw during the head-raising motion. Finally, the head-raising motion is simulated using the angle sequences to validate the feasibility of this method.