Despite the growing popularity of reinforced concrete (RC) core walls, robust uncertainty quantification of their global and local performances remains an intractable challenge. A combination of a random sampling technique in conjunction with a simplified structural analysis has been widely used, but substantial ambiguity remains in the simulation accuracy and the resultant uncertainties. As a fast and robust alternative, this study suggests a moment matching (MM) technique. MM can dramatically reduce required sample points to only a few, which enables a direct use of a high-precision parallel multiscale finite element analysis (PM-FEA) for uncertainty quantification. This study demonstrates how to apply the combination of MM and PM-FEA to quantify uncertainties behind complex RC core walls, notably in terms of global force-resisting capacity and microscopic progressive bar buckling of five U-shaped walls. Results suggest that the combination of MM and PM-FEA will serve as a promising method to improve our understanding of uncertainties behind complex RC structure.