The distribution of stiffeners in the stiffened plate structure seriously affects its structural performance. At present, most of the work on the design of the stiffened plate structure is carried out under deterministic load conditions, where the effect of load uncertainty on the structural stiffness is ignored. This paper proposes a robust structural layout optimization method for layout optimization problem of stiffeners in stiffened plate structures considering load uncertainty, and realizes the simultaneous optimization of the layout and size of stiffeners. A robust layout optimization model is established based on the ground structure method, with the radius of the circular section beam representing the stiffener as the design variable, the mass of the entire structure as the constraint, and the linear weighted value of the expected and variance of the structural compliance under uncertain loads as the objective. The analytical sensitivity formula of the expectation and variance of the structural compliance and the mass constraint with respect to design variables are deduced in detail. The method of moving asymptotes is adopted to solve the robust layout optimization problem. Finally, two examples are performed to verify the effectiveness of the proposed method.