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A large scale low-profile traveling-wave narrow-wall slotted waveguide array with 2160 slots is analyzed by parallel method of moments (MoM) out-of-core solver based on the higher order basis functions (HOBs). Its accuracy is validated through comparison with the finite element method (FEM) adopted in the commercial software Ansoft HFSS. An out-of-core two-dimensional block-cyclic distribution scheme for the large dense full matrix filling and an out-of-core LU (lower/upper) decomposition matrix equation solver are utilized under the message passing interface (MPI). Numerical results are shown to demonstrate the memory cost effectiveness, time efficiency of the proposed method and its applicability. The method presented in this paper is able to solve challenging realistic problems in large scale.