This Letter demonstrates tunable Nb5N6 microbolometers operating in the terahertz frequency range. An asymmetric-coupled Fabry-Pérot cavity is constituted by simply placing a movable metallic planar mirror in the back of the silicon substrate. The incident THz radiation onto the Nb5N6 microbolometer is effectively manipulated by changing the air spacer gap to modulate the phase relation between the reflected wave and incident wave. The experimental measurements reveal that the detailed evolution of the resonance bands as a function of spacing is in excellent agreement with the analysis by using interference theory and simulation. The results detail the design of THz detectors wherein a wide degree of tunability or a variable number of detection bands is desirable.