A　type　of　parallel　augmented　subspace　scheme　for　eigenvalue　problems　is　proposed　by　using　coarse　space　in　the　multigrid　method.　With　the　help　of　coarse　space　in　the　multigrid　method,　solving　the　eigenvalue　problem　in　the　finest　space　is　decomposed　into　solving　the　standard　linear　boundary　value　problems　and　very-low-dimensional　eigenvalue　problems.　The　computational　efficiency　can　be　improved　since　there　is　no　direct　eigenvalue　solving　in　the　finest　space　and　the　multigrid　method　can　act　as　the　solver　for　the　deduced　linear　boundary　value　problems.　Furthermore,　for　different　eigenvalues,　the　corresponding　boundary　value　problem　and　low-dimensional　eigenvalue　problem　can　be　solved　in　the　parallel　way　since　they　are　independent　of　each　other　and　there　exists　no　data　exchanging.　This　property　means　that　we　do　not　need　to　do　the　orthogonalization　in　the　highest-dimensional　spaces.　This　is　the　main　aim　of　this　paper　since　avoiding　orthogonalization　can　improve　the　scalability　of　the　proposed　numerical　method.　Some　numerical　examples　are　provided　to　validate　the　proposed　parallel　augmented　subspace　method.　©　2020　Society　for　Industrial　and　Applied　Mathematics