An analytical solution for contaminant transport through a vertical cut-off wall and aquifer system is developed, which can consider the advection, dispersion and degradation processes. The uniqueness of the solution is that it includes hyperbolic eigenfunctions, considers the degradation process and is suitable for an aquifer with finite thickness due to the existence of a river or lake. The solution is first verified against an existing analytical solution and a numerical model using the Comsol software program. The three important aspects are then investigated and some important conclusions are obtained. In some scenarios, the hyperbolic eigenfunctions must be considered; otherwise, the obtained results are unreasonable. When the aquifer thickness is more than a critical value (approximately ten times the cut-off wall thickness in this study), it is reasonable to regard the aquifer as semi-infinite. Contaminant degradation has significant influence on contaminant transport. A higher degradation intensity leads to a lower contaminant concentration but a larger mass flux in the cut-off wall. Therefore, the present solution is suitable for an aquifer with arbitrary thickness and has better applicability than the existing analytical solutions. It is promising to be used as an applicable tool for the design of vertical slurry cut-off walls.