The functional renormalization group-aided density-functional analysis (FRG-DFT) starts to be applied to realistic models of quantum many-body systems. Recently we have developed a new FRG-DFT formalism, which is suitable for analyzing systems with an infinite number of particles with fixed densities. In this talk, I will present our formalism and our two applications: The first one is the calculation of the equation of state (EOS) and the density-density spectral function of an infinite nuclear matter (NM) in (1+1) dimensions composed of spinless nucleons. The resultant EOS of the NM coincides with that obtained by the Monte-Carlo method within a few percents for the available range of density. We also reproduce a notable feature of the density spectral function of the non-linear Tomonaga-Luttinger liquid: The spectral function has singularities at the edge of its support at the lower-energy side. Subsequently, I will show our FRG-DFT analysis of the two-dimensional homogeneous electron gas, which is the first application of FRG-DFT to two-dimensional systems. We find that the result of FRG-DFT reproduces the exact correlation energy at the high-density limit and is consistent with the Monte-Carlo results for the high- and mid-density cases. Our study demonstrates that the FRG-DFT can be a promising method to analyze quantum many-body systems.