For a one-dimensional nonlinear pseudoparabolic equation we consider its initial boundary value problem on an interval. The boundary condition on the left endpoint is of Dirichlet type, but the condition on the right endpoint is replaced by a nonlocal one. Because it is given by an integral, the function involved could exhibit singularities, which distinguishes this nonlocal condition from its Dirichlet counterpart. Based on an elliptic estimate and an iteration method we established the well-posedness of solutions in a weighted Sobolev space.