According to a series of hypothesis, for the spiral galaxy, a mathematical equation of the graviton movement track is built, it is also the central curve of the nebulae density distribution, which offers the method to measure the moving speed of the graviton. Using the observed images of the M51 galaxy, it confirms that the graviton movement curve in the spiral galaxy conforms to the image, QUOTE QUOTEis a constant. It points out that by measuring the rate of angular motion of the equivalent center in the galaxy, the real speed of the graviton can be estimated. Under the measuring condition of the M51,. The theory presented in this article also helps to calculate the rotation speed of a galaxy, provided the graviton speed is known for certain. With the model in this article and fitting data from the observation images of M51 galaxy, the guess which says “the moving speed of graviton is a constant” is supported unprecedentedly by observation data. It is for the first time that the upper limit of graviton speed, i.e. no more than times of light speed, is obtained from observation data. At the same time, the paper puts forward one possible way that the lower limit of graviton speed may be measured. And a new idea also brought forward in the paper is that the rotational angular velocity w of the equivalent center which plays an important role in a spiral galaxy may be measured according to the observed data of the thickness of galactic center of the spiral galaxy.