Aiming at the intrinsic coupling relationship between investors and the difference on the investors’ information cognition and disposition, evolution model of rumor spreading is constructed by considering the investors’ amnestic behavior and memory behavior on rumor spreading. By applying theoretical and simulation analysis, the authors get such results that infectious index, the network connection strength and network topology structure directly influence the rumors spreading in stock markets threshold characteristics and evolution stability; there exists a rumor transmission threshold of the SIHR evolution model on weighted investors’ relationship networks; compared to the connection intensity index, transmission index places more important impact on rumor spreading in stock markets.