In recent years, solar energy has become popular because of its clean and renewable properties. Meanwhile, two-dimensional materials have become a new favorite in scientific research due to their unique physicochemical properties. Among them, monolayer molybdenum disulfide (MoS2), as an outstanding representative of transition metal sulfides, is a hot research topic after graphene. Therefore, we have conducted an in-depth theoretical study and design simulation using the finite-difference method in time domain (FDTD) for a solar absorber based on the two-dimensional material MoS2. In this paper, a broadband solar absorber and thermal emitter based on a single layer of molybdenum disulfide is designed. It is shown that the broadband absorption of the absorber is mainly due to the propagating plasma resonance on the metal surface of the patterned layer and the localized surface plasma resonance excited in the adjacent patterned air cavity. The research results show that the designed structure boasts an exceptional broadband performance, achieving an ultra-wide spectral range spanning 2040 nm, with an overall absorption efficiency exceeding 90%. Notably, it maintains an average absorption rate of 94.61% across its spectrum, and in a narrow bandwidth centered at 303 nm, it demonstrates a near-unity absorption rate, surpassing 99%, underscoring its remarkable absorptive capabilities. The weighted average absorption rate of the whole wavelength range (280 nm–2500 nm) at AM1.5 is above 95.03%, and even at the extreme temperature of up to 1500 K, its heat radiation efficiency is high. Furthermore, the solar absorber in question exhibits polarization insensitivity, ensuring its performance is not influenced by the orientation of incident light. These advantages can enable our absorber to be widely used in solar thermal photovoltaics and other fields and provide new ideas for broadband absorbers based on two-dimensional materials.