The Springer variety of type A associated to a nilpotent operator on C-n in Jordan canonical form admits a natural action of the l-dimensional torus T-l where l is the number of the Jordan blocks. We give a presentation of the T-l-equivariant cohomology ring of the Springer variety through an explicit construction of an action of the n-th symmetric group on the T-l-equivariant cohomology. The T-l-equivariant analogue of so-called Tanisaki's ideal will appear in the presentation. (C) 2016 Elsevier B.V. All rights reserved.