We present for the first time to our knowledge a new and simple single-mode optical-fiber double-loop resonator. The double-loop resonator consists of two fiber loops constructed from a nonplanar 3 x 3 directional fiber coupler and two fiber delay lines. When the lengths of the fiber loops are different, additional periodic-resonance notches appear. The depths and the positions of these notches depend on the difference between the phase changes, and the coupling of the two fiber loops. This double-loop resonator can be used as a spectral filter and a sensor.