A sandwich structure of dielectric material and air gap inside a rectangular waveguide is proposed as a fast electrically tunable low-loss phase shifter. As the dielectric material is shifted up and down by piezoelectric actuator and, thereby, the thickness of air gap is changed, the effective dielectric constant of the sandwich structure is varied. Phase shifters based on the sandwich structure with different dielectric materials showed phase shift of $20{sim}200^{circ}/cm$ at X-band as the thickness of air gap varied up to $30{mu}m$. The idea can be extended toward low-loss millimeter wave phase shifters since modem microwave ceramics have been developed to show very low dielectric loss$(tan;{delta}{sim}10^{-4})$.