We establish a finite element multigrid discretization scheme based on the shifted-inverse iteration for the Steklov-Lamé eigenproblem, and investigate the a posteriori error estimation of residual type for the scheme. Firstly, we give the error estimation of the approximate eigenfunction in the sense of L²(∂Ω) norm, then we give the a posteriori error indicators for the multigrid approximate solution, and prove the reliability and efficiency of the indicators. Finally, we use the a posteriori error indicators to design an adaptive multigrid algorithm for solving the Steklov-Lamé eigenproblem.