Nowadays, density functional theory (DFT) is a strong theoretical tool applicable to researches on biomolecule and material sciences. In particular, hybrid DFT functionals initiated active chemical applications of DFT, in that it can reproduce energy and property of finite systems within chemical accuracy as well as with low computational cost compared with wave function theory. However, in spite of its high applicability, DFT has shown severe inappropriateness of producing some following basic properties: inter- and intra-molecular van der Waals interaction, inter- and intra-molecular charge transfer excitation energy and its oscillator strength, (hyper-)polarizability, isomerization energy of organic molecules, core-excitation energy, HOMO-LUMO gaps of molecules, and so on. As a result of our efforts to solve these problems, we proposed a new hybrid functional named long-range corrected (LC) DFT and showed successful improvement on the problems mentioned above.[1] It is well known that still high demanding of time cost to evaluate long-range HF exchange is a big obstacle for LC-DFT to be applied to large molecular systems and solid state materials. Unlike acceleration methods for Coulomb integration, such as fast multipole method, developing acceleration methods for the HF exchange is still a pioneering area. We will show our recent progress against this problem, specially on developing a new linear-scaling method of HF exchange integration for LC-DFT hybrid functional.[2] Additionally, we will present the recent results of linear-scaled LC-DFT on adsorption energy between CO molecule and Cu surface. [1] J.-W. Song, T. Hirosawa, T. Tsuneda, and K. Hirao, J. Chem. Phys. 126, 154105 (2007). [2] J.-W. Song and K. Hirao, J. Chem. Phys. 143, 144112 (2015).