We studied on terahertz-quantum cascade lasers (THz-QCLs) using III-Nitride semiconductors, which are promising materials for the realization of the unexplored frequency range from 5 to 12 THz and the higher temperature operation on THz-QCLs, because these compounds have much larger longitudinal optical phonon energies (> 18 THz) than those of conventional GaAs-based materials (~ 9 THz). Firstly, we showed clearly that it is possible to design a GaN-based quantum cascade (QC) structure which operates in the THz range in which population inversion can be obtained, by performing numerical calculations based on a self-consistent rate equation model. Secondly, we succeeded in the stack of QC structure with a large number of periods and the drastic improvement of structural properties of QC structure, by introducing a new growth technique named "a droplet elimination by thermal annealing (DETA)" in which utilized the differences of the properties between metals (Al, Ga) and Nitrides (AlN, GaN) into molecular beam epitaxy. Finally, we for the first time successfully observed spontaneous electroluminescence due to intersubband transitions with peaks at frequencies from 1.4 to 2.8 THz from GaN/AlGaN QCL devices fabricated with using the DETA technique grown on a GaN substrate and a metal organic chemical vapor deposition (MOCVD)-AlN template on a sapphire substrate. In this paper, we demonstrate recent achievements on the quantum design, fabrication technique, and electroluminescence properties of GaN-based QCL structures.