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Monolayer MoS2 has excellent optical properties, but its low optical absorption hinders its application in optical absorbers. To improve its absorption performance, we design an aperiodic multilayer structure with monolayer MoS2, the dielectric materials Si and SiO2 arranged by Kolakoski sequence, and achieve the perfect absorption in the visible wavelength range because of its omnidirectional reflectivity. By optimizing the thicknesses of SiO2 (db), Si (dc) and the repetition number (N) of the unit cell, the absorption of the aperiodic multilayer structure can be greatly improved at normal incidence. When N is 3, this aperiodic multilayer structure achieves high absorption of up to 98% in the wavelength range from 350 to 450 nm. As N increases to 5 or 7, the average absorption of this aperiodic multilayer structure exceeds 90% in the 350–600 nm wavelength range. In addition, we verify that the broadband and high absorption obtained in this aperiodic multilayer structure is robust against the angle of incidence and polarization of the incident wave. Our results suggest an alternative configuration with monolayer MoS2 to realize the broadband and perfect absorption, which is useful for future applications in solar cell or photodetectors. [ABSTRACT FROM AUTHOR]