The safety evaluation of engineering systems whose performance evaluation requires finite element analysis is a challenge in reliability theory. Recently, Adjusted Control Variates Technique (ACVAT) has proposed by the authors to solve this issue. ACVAT uses the results of a finite element method (FEM) model with coarse mesh density as the control variates of the model with fine mesh and efficiently solves FEM-based reliability problems. ACVAT however does not provide any results about the reliability-based mesh convergence of the problem, which is an important tool in FEM. Mesh-refinement analysis allows checking whether the numerical solution is sufficiently accurate, even though the exact solution is unknown. In this study, by introducing expanded control variates (ECV) formulation, ACVAT is improved and the capabilities of the method are also extended for efficient reliability mesh convergence analysis of FEM-based reliability problems. In the present study, the FEM-based reliability analyses of four practical engineering problems are investigated by this method and the corresponding results are compared with accurate results obtained by analytical solutions for two problems. The results confirm that the proposed approach not only handles the mesh refinement progress with the required accuracy, but it also reduces considerably the computational cost of FEM-based reliability problems.