In this paper an innovation of satellite positioning system is presented. The scheme of designing low Earth orbit (LEO) satellite positioning system is proposed. An example LEO satellite constellation providing the positioning function over certain region is given. The proposed constellation consists of 75 satellite orbits at four different inclinations. The satellites are in the orbit of height of about 800 km. They can provide the positioning function over the region with radius of about 3000 km centered at the point with longitude of 122∘E and latitude of 25∘N. The structure of the constellation is based on the requirements of good values of the dilution of precision (DOP) calculated over the specific region. For completeness, the study of the relativistic effects of the system is also given. Based on the result, it shows that the requirement of keeping the orbit of the LEO satellite positioning system is less stringent. As a result, the system provides an alternative of positioning function for regional use.