Group　activity　recognition　can　remarkably　improve　the　understanding　of　video　content　by　analyzing　human　behaviors　and　activities　in　videos.　We　propose　a　random　walk　graph　convolutional　network　(RWGCN)　for　group　activity　recognition.　(1)　Considering　the　limitation　of　the　convolutional　structure　to　the　visual　information　of　group　activities,　the　position　feature　extraction　module　is　used　to　compensate　for　the　loss　of　visual　information.　(2)　A　graph　convolutional　network　(GCN)　with　distance-adaptive　edge　relations　is　constructed　using　individuals　as　graph　nodes　to　identify　the　intrinsic　relationships　among　the　individuals　in　the　group　activities.　(3)　A　Levy　flight　random　walk　mechanism　is　introduced　into　the　GCN　to　obtain　information　from　different　nodes　and　integrate　the　previous　position　information　to　recognize　group　activity.　Extensive　experiments　on　the　publicly　available　CAD,　CAE　datasets,　and　self-built　BJUT-GAD　dataset　show　that　our　RWGCN　achieves　MPCA　of　95.49%,　94.82%,　and　96.02%,　respectively,　which　provides　a　better　competitiveness　in　group　activity　recognition　compared　to　other　methods.