Least　squares　regression　is　a　fundamental　tool　in　statistical　analysis　and　is　more　effective　than　some　complicated　models　with　small　number　of　training　samples.　Representing　multidimensional　data　with　product　Grassmann　manifold　has　recently　led　to　notable　results　in　various　visual　recognition　tasks.　This　paper　proposes　extrinsic　least　squares　regression　with　ProjectionMetric　on　product　Grassmann　manifold　by　embedding　Grassmann　manifold　into　the　space　of　symmetric　matrices　via　an　isometric　mapping.　The　proposed　regression　has　closed-form　solution　which　is　more　accurate　compared　with　numerical　solution　of　previous　least　squares　regression　using　geodesic　distance.　Experiments　on　several　recognition　tasks　show　that　the　proposedmethod　achieves　considerable　accuracy　in　comparison　with　some　state-of-the-art　methods.