This paper presents a hybrid method for fast analysis of electromagnetic (EM) scattering from large-scale aperiodic structures (e.g., Penrose and Danzer tilings), which integrates the characteristic basis function method (CBFM) and the adaptive integral method (AIM). The CBFs defined on the macro block facilitate a substantial reduction in the method of moments (MoM) matrix size, enabling the use of direct solvers for large problems. The initial CBFs are constructed by illuminating one block with θ- and -polarization plane waves for multiple incident angles. Thereafter, the singular value decomposition (SVD) method and threshold are used to extract the independent basis from the initial solution space, ultimately leading to the final CBFs. The AIM is applied to accelerate the calculation of CBFM reduced MoM matrices, significantly decreasing the CPU time and memory required for solving large-scale problems. As the size of one block becomes electrically large, the original CBFM combined with AIM is employed to generate the initial CBFs by solving a problem with multiple excitations, which results in efficiently constructing the final CBFs afforded by the SVD procedure. After validating the developed code, the subsequent solver is applied to investigate EM scattering from large-scale aperiodic tilings in order to demonstrate the efficiency of the proposed method. Further, the numerical results show that Penrose and Danzer tilings exhibit improved grating lobe suppression as compared to their periodic counterparts.