A matrix representation of the super symmetry is introduced, based on the superfield formulation. The group structure of the finite supertransformations is shown to be closely connected with this representation, and a 16-component covariant derivative is naturally intro­ duced in this context. Applying this representation to the supersymmetric gauge theory we calculate some supergraphs and get the results which agree with those obtained by using the superfield method. The calculations in our representation are, however, considerably simplified compared with the superfield ones. Moreover, it is shown in the one loop level that the cancellation of the ultraviolet divergences of the supergraphs is due to the structure of the finite supertransformations.