In this paper, asymmetric drainage boundaries modeled by exponential functions which can simulate intermediate drainage from pervious to impervious boundary is proposed for the one-dimensional consolidation problem, and the solution for the new boundary conditions was derived. The new boundary conditions satisfy the initial and the steady state conditions, and the solution for the new boundary conditions can be degraded to the conventional solution by Terzaghi. Convergence study on the infinite series solution showed that only one term in the series is needed to meet the precision requirement for larger degree of consolidation, and that more terms in the series for smaller degree of consolidation. Comparisons between the present solution with those by Terzaghi and Gray are also provided. © 2014 Techno-Press, Ltd.