In this paper, a high-order iterative scheme is established for a nonlinear Love equation associated with homogeneous Dirichlet boundary conditions. This is a development based on recent results (L.T.P.Ngoc, N.T. Long (2011); L.X.Truong, L.T. P.Ngoc, N.T. Long (2009)) to get a convergent sequence at a rate of order N ⩾ 2 to a local unique weak solution of the above mentioned equation.