Compared with medium Earth orbit (MEO) and high Earth orbit (HEO) satellites, low Earth orbit (LEO) satellites have lower cost, smaller power loss and shorter transmission delay, which mean they can be used in many areas like navigation and space-based internet of things (IOT), etc. However, when LEO satellites are applied to navigation, there will be a large quantity of satellites in the constellation leading to large solution space, which makes LEO global navigation constellation design complicated. In this paper, constraints for constellation design including the ranges of constellation height, minimum observation elevations, coverage multiple, the number of satellites and the dilution of precision (DOP) value are considered. To effectively achieve global navigation with LEO satellite, the street of coverage (SOC) method was used to analyze the Walker constellation. Then, a LEO satellite constellation design method was proposed for quadruple coverage. The results show that the designed LEO constellation satisfies the global quadruple coverage constraint. Meanwhile, the position dilution of precision (PDOP) available area ratio stays above 98.9% when the threshold is 8, and stays above 94% when the threshold is 4. These verified the feasibility and effectiveness of the design.