<p>In this paper, the barycentric Lagrange interpolation collocation method is employed to solve a class of nonlinear fractional pseudo-parabolic equations. First, the Gaussian quadrature formula is applied to approximate the fractional term, and two iterative schemes—direct linearization and partial linearization—are constructed to handle the nonlinear term. Subsequently, a matrix equation is derived based on the discrete formulation, and iterative computations are performed after incorporating the initial and boundary conditions. Finally, several numerical examples are presented to demonstrate the efficiency and accuracy of the proposed method in solving this type of equations.</p>