Node localization is the core in wireless sensor network. It can be solved by powerful beacons, which are equipped with global positioning system devices to know their location information. In this paper, they present a novel sparse localization approach with a mobile beacon based on LU decomposition. Their scheme firstly translates node localization problem into a 1-sparse vector recovery problem by establishing sparse localization model. Then, LU decomposition pre-processing is adopted to solve the problem that measurement matrix does not meet the restricted isometry property. Later, the 1-sparse vector can be exactly recovered by compressive sensing.