Information design involves a designer with the goal of influencing players’ actions in an incomplete information game through signals generated from a designed probability distribution so that its objective function is optimized. We consider a setting in which the designer has partial knowledge on players’ payoffs, and wants to maximize social welfare. We address the uncertainty about players’ preferences by formulating a robust information design problem against the worst-case payoffs. When the players have quadratic payoffs that depend on the actions and an unknown payoff-relevant state, and signals on the state that follow a Gaussian distribution, the information design problem under quadratic design objectives can be stated as a semidefinite program (SDP) (Ui, 2020). Given this fact, we consider ellipsoid perturbations over payoff coefficients in linear-quadratic-Gaussian (LQG) games. We show that we can obtain a similar SDP formulation that approximates the social welfare maximization via robust information design. Numerical experiments identify the relation between the uncertainty level on players’ payoffs and the optimal information structures.