In combination with kinetic models of mineral dissolution-precipitation, numerical simulation of calcite dissolution-precipitation and solute transport in an investigative zone is accomplished in this paper in order to study the variation law of mineral dissolution-precipitation and the effect of solute transport. The main conclusions are drawn as follows: 1) distribution of solute transport is discontinuous because of the effect of fracture network distribution and the solute transportation is mainly through the connected fracture network from upstream to downstream; 2) concentration increases in the dissolute zone and decreases in the precipitate zone when considering the calcite dissolution-precipitation; and 3) the dissolution-precipitation of calcite is mainly influenced by concentration of CO2-3 ion.