Hexagonal rare-earth ferrites (h-RFeO3) are promising multiferroic materials owing to the spontaneous magnetization, high ferroelectric transition temperature, and fascinating features provided by strong magnetoelectric coupling. However, h-RFeO3 is metastable, and its synthetic methods are limited, particularly when ionic size of R is large. One of useful synthesis methods is epitaxial thin-film growth on single-crystal substrates, because the metastable phase is stabilized by the lattice match between h-RFeO3 and the substrate. Compared to single-crystal substrates, glass substrates are more cost-effective. However, films on glass tend to consist of a thermodynamically stable phase owing to the amorphous nature of glass substrates. Herein, we report that a h-RFeO3 pure phase can be obtained as thin film even on glass substrates. The metastable phase was formed owing to the nonequilibrium synthesis process of pulsed laser deposition. The obtained h-RFeO3 thin films on glass with R = Dy, Er, and Lu exhibited weak ferromagnetism with Néel temperatures of 120–140 K. Furthermore, a clear magnetic phase transition from weak ferromagnetic to antiferromagnetic phase was observed in the h-ErFeO3 films. Additionally, piezoelectric force microscopy measurements exhibited the ferroelectricity of the film at room temperature. These results provide a convenient synthesis method of a pure phase multiferroic h-RFeO3 system.