Singular systems are dynamical systems subject to algebraic constraints, and arise in many engineering disciplines. The output regulation problem for singular nonlinear systems has been studied recently for the ideal case where the mathematical model is exactly known. This paper will further consider the robust output regulation problem for a class of singular nonlinear systems which contain uncertain parameters. It will establish the conditions for the solvability of the problem, thus extending the existing results from the normal nonlinear systems to the singular nonlinear systems.