Abstract. Static antiferromagnetic (AF) spin correlations of overdoped La2-xSrxCuO4 (LSCO) with and without Zn doping have been studied by neutron scattering. In a single crystal of Zn-free LSCO for x=0.21, no elastic magnetic signals were observed even at 80mK. However, elastic signals appear below 22K in 1% Zn-doped LSCO for x=0.21, indicating that Zn stabilizes the static AF spin correlations even in the overdoped LSCO. The present study confirmed that the AF propagation wave vector is incommensurate with the lattice, characterized as QAF=(1/21/20) with =0.005(2) and =0.135(2). The appearance temperature (Tm) of the elastic signal degrades under higher-energy resolution, suggesting that the static correlations induced by Zn have a spin-glass-like nature.