In the present study, method of temporal moments has been used to analyse the transport characteristics of reactive solute along fracture in a coupled fracture-skin-matrix system. In order to obtain the concentration distribution within the fracture, a system of coupled partial differential equations for fracture, fracture-skin and rock-matrix has been solved numerically in a pseudo two-dimensional domain using implicit finite difference method. Subsequently, lower order temporal moments of solute have been computed from the concentration distribution to analyse the transport characteristics of solutes in the fracture. This study has been done by considering an inlet boundary condition of constant continuous source in a single fracture. The effect of various fracture-skin parameters like porosity, thickness and diffusion coefficient on the transport of solutes have been studied by doing sensitivity analyses. The effect of nonlinear sorption and radioactive decay of solutes have also been analysed by carrying out simulations for different sorption intensities and decay constants. Numerical results suggested that the presence of fracture-skin significantly influences the transport characteristics of reactive solutes along the fracture. © 2014 Indian Academy of Sciences.