In this letter, a novel solution method of generalized robust chance constrained real-time dispatch (GRCC-RTD) considering wind power uncertainty is proposed. GRCC models are advantageous in dealing with distributional uncertainty, however, they are difficult to solve because of the complex ambiguity set. By constructing traceable counterparts of the robust chance constraints and using the reformulation linearization technique, the model is equivalently transformed into a deterministic linear programming problem, which can be solved efficiently by off-the-shelf solvers. Numerical results verify the effectiveness and efficiency of the approach.