It has been gradually recognized of the existing of initial hydraulic gradient（i₀）during water seepage in soft clay and the necessity of considering continuous drainage boundary is being accepted more and more. However, the analytical solution of one-dimensional consolidation under variable load, considering both continuous drainage boundary condition and initial hydraulic gradient has rarely been reported. Based on the actual situation that the external load increases with time, taking variable load into account, a consolidation model considering both continuous drainage boundary and initial hydraulic gradient is established. The approximate analytical solution of the one-dimensional consolidation model is obtained by using Fourier transform and Laplace transform, from which, the moving law of dynamic boundary, dissipation law of excess pore water pressure as well as the growth characteristics of average consolidation degree are analyzed. The results show that, with the same loading rate, the influence of permeability of drainage surface under initial hydraulic gradient on consolidation behavior is just the same with that according to Darcy's law. The better the permeability is, the faster the dissipation rate of pore water pressure comes, and conversely, the worse the permeability is, the slower the dissipation rate of excess pore water pressure becomes. The effect of initial hydraulic gradient on consolidation behavior under continuous drainage boundary presents consistent with that under fully permeable boundary, of which the fact is, a larger value of i₀ may lead to, larger residual excess pore pressure when consolidation is completed, and smaller average degree of consolidation defined by pore pressure. On the other side, the smaller value of i₀ is, the shorter time it takes for the moving boundary reaching to the bottom of soil layer, the smaller the residual excess pore pressure becomes, and the larger the average degree of consolidation defined by pore pressure is. When under the same initial hydraulic gradient case and boundary drainage conditions, the peak value of excess pore water pressure decreases with the growth of loading time, and correspondingly takes longer time for the excess pore water pressure reaching to the peak value. However, the loading time has no influence on the residual value of excess pore water pressure and the final average cohesion defined by pore pressure.