In order to explore the influence of microfracture development caused by chemical dissolution on the mechanical properties of limestone, this paper presents a new numerical simulation and quantitative analysis method. At first, the dissolution rate was determined by the theory of chemical kinetics and a differential equation that can be solved for results of the fracture evolution process by COMSOL Multiphysics was established to describe the microfracture's expansion. The fractal dimensions of the microfractures were found to have a linear relationship with the damage variables at different time periods through analysis of the simulation results with the fractal geometry method using fracture width as the index, which proves that the evolution of damage has the fractal feature. After that, a damage evolution equation was fitted to predict the deterioration in rock mechanical properties under the hydro-chemical actions and the predictive uniaxial compressive strength of limestone is seen to be in favorable agreement with experimental test results. The application of the fractal geometry method has important engineering significance since it reflects development in the microscopic fractures to changes in the macroscopic mechanical properties and realizes the prediction of the mechanical properties of the rock under chemical damage.