Premixed flame propagation within a narrow combustion space has been an important issue in combustion studies. Recently, it was found that flame-induced instabilities are very sensitive to the length-scale of the combustion space. However, experimental results obtained at higher pressures have not been sufficient. In this study, the propagation characteristics of methane and propane premixed flames were investigated using a new narrow-gap disk burner, of which the disk gap and the initial pressure could be varied precisely while the volume was kept constant. Quenching distances were measured during increase of the initial pressure to 4 bar. Flame propagation characteristics were compared with variation of the disk gap, the equivalence ratio, and the initial pressure. Significant changes were found in the trends of the flame propagation velocity and flame shape. Cellular flame structures were observed when the disk gap was slightly larger than the quenching distance regardless of the Lewis number. In contrast, smooth flames could form when the disk gap was sufficiently larger than the quenching distance. The elevated pressure enhanced flame oscillation and cellular structures (if they could be generated) regardless of Lewis number of mixtures. The relationship between the pressure and the flame propagation was evaluated, and a mechanism for the flame instability is discussed herein.