Stress singularity is usually observed in practical stress analysis, and it may lead to the deterioration of the convergence rate of the preconditioned conjugate gradient method (PCG). Until now, parallel PCG has been used without considering the practical issues; therefore, the deterioration was induced in the problem in which stress singularity was observed. The convergence acceleration method was developed in parallel PCG based on controlled domain decomposition. The acceleration method can be achieved by considering the spatial locality of stress singularity and preconditioning of conjugate gradient method. The convergence acceleration method reduces the 15% of iteration of PCG as a maximum, where the singular area is included in one domain.