A newly developed version of a three-dimensional computer model for simulating the hydration and microstructure development of slag cement pastes is presented in this study. It is based on a 3-D computer model for Portland cement hydration (CEMHYD3D) which was originally developed at NIST, taken over in the authors’ group and further developed. Features like the digitized 3-D microstructure, the cellular automata (CA) algorithm for simulating the random walking, phase transformation for simulating the chemical reactions, are retained. But, the 3-D microstructure was reconstructed allowing for slag particles as binder in the system. Algorithms and rules are developed to account for the interaction between Portland cement hydration and slag reaction in the paste, of which the mechanisms were revealed in the studies by Chen and Brouwers [(2007) J Mater Sci 42(2):428; (2007) J Mater Sci 42(2):444] Methods for considering the various factors on the reactivity of slag in hydrating slag cement pastes are proposed, mainly for the oxide composition of slag and the alkalinity in the pore solution composition. A comparison between the model predictions and the experimental results in literature shows that the presented computer model can successfully predict the hydration process and the microstructure development of hydrating slag cement paste.