A finite-element method study was conducted on a laboratory-scale partially premixed combustor, for investigating the characteristics of combustion instability due to fuel composition variations. The authors’ previous studies reported frequency mode shifting in the same combustor with hydrogen enrichment, and the cause of this phenomenon was analyzed only from the viewpoint of the flame shape change and time lag theory. An increase in hydrogen fraction results in an increase in the speed of sound in the fuel feeding line, resulting in an increase in resonant frequencies determined by the fuel line geometry. This analysis shows that the hydrogen enrichment increases the bulk and longitudinal resonant frequencies of the fuel feeding line. When one of these fuel line resonances is coupled with the intrinsic acoustic mode of the combustor, the hydrogen fraction can be one of the key parameters affecting the main characteristics of combustion instability in a partially premixed system.