We investigate the structure of an infinite-dimensional symmetry of the four-dimensional Kahler WZW model, which is a possible extension of the two-dimensional WZW model. We consider the SL(2, R) group and, using the Gauss decomposition method, we derive a current algebra identified with a two-toroidal Lie algebra, a generalization of the affine Kac-Moody algebra. We also give an expression of the energy-momentum tensor in terms of currents and extra terms.