Whether or not you can transplant a concord grape vine depends in large measure on how old your grape vine is. Older vines have larger and more complex root systems than do younger vines, and the loss of too much of the root system is the major reason that some grape vines do not make it when transplanted. Great care must be taken when digging out your old vine to get as many of the roots as possible and when replanting the hole must be dug deep enough and wide enough to accommodate the roots without bending, breaking or trimming them. The best time to transplant a concord grape vine is in early spring, while the vine is still dormant but the soil is not frozen. This allows the vine a full growing season to establish a new root system before winter arrives.
Choose a place for your concord grape vine to be transplanted to. Choose a sunny location with well-drained soil.
Prune back the vine you are about to transplant. Prune it back to one primary cane so there will be as little loss of water through the leaves as possible after the vine is transplanted.
Carefully dig up the concord grape vine which you wish to transplant. Begin digging at least three feet away from the main trunk and dig carefully, looking for roots as you go. If the roots extend past the point at which you have begun digging then dig further away from the vine. Keep as many of the roots intact as possible.
Gently lift the vine out of the hole you have just dug and lay the vine on a flat surface with the roots dangling over an edge so they will not be bent or broken. Wrap the roots in burlap immediately and dampen the burlap well. Do not let the roots dry out.
Place a large tub, large enough to hold all of the vine's roots, on a cart for transporting the vine and fill the tub with water. Place the burlap-wrapped roots in the tub of water and transport the vine to its new location. If it is not possible to transport a water-filled tub to the new location, transport the vine with the burlap kept damp and then place the vine's roots in a tub of water at the replanting location. Keep the vine's roots in water for at least 6 hours before replanting.
Dig a hole large enough to accept the entire root ball of the vine without bending, breaking or cutting any of the roots. Do not make the root ball accommodate the hole you have dug--make the hole accommodate the vine's root ball.
Place the grapevine's root ball in the hole and fill it with soil, adjusting as you go so that when done the grapevine is at the same position with respect to the soil level as it was in its old spot. Pack the soil firmly but not so firmly as to risk damaging the roots. Do NOT add any fertilizer as that will burn the sensitive roots.
Water well and keep the soil damp but not soggy for two to three months, until new growth is seen on the vine. Then water normally.