<p>In this work, we show that a global martingale solution exists to a stochastic degenerate cross-diffusion system. Previous results showed that for some stochastic cross-diffusion systems without degeneration, martingale solutions exist. The existence of a martingale solution has to be shown under an upgraded tightness proof scheme if the degenerate factor is involved. We rely on a regularization of the entropy variable method to derive the sequence of approximated solutions, then to show its limit is a martingale solution of the system. Once the diffusion matrix of the cross-diffusion system does not satisfy assumptions for applying this regularization of the entropy variable method, we have to regularize the diffusion matrix to derive approximated solutions.</p>