Abstract: The spatial position uncertainty influences the availability of the vector spatial data, which is directly controlled by the two-dimensional probability distribution model of the point's position errors. This paper studies the spatial distribution model of GPS RTK positioning random error, which has repeatedly measured the selected points for 20 days. Then the one-and two-dimensional normal distribution tests and two-dimensional normal distribution fitting are employed to analyze the distribution model. The results show that the GPS RTK positioning random error fits directional two-dimensional normal distribution model and the significance is enhanced constantly along with the observation time shorten. The research results can build foundation for analyzing the influencing factors of the distribution model of positioning random error and establishing the mathematic forecasting model. Besides, contribute to promote the theoretical research of position uncertainty for spatial vector data.