Third-order random lasing operating in 1670 nm spectral band is experimentally demonstrated for the first time to the best of our knowledge, with only 2.45 W pump threshold. The lasing cavity is formed by G.652 fiber and fiber loop mirrors (FLMs), while the former acts as the distributed reflector and the latter acts as the point reflector. The G.652 fiber and the FLMs are connected via a multi-band wavelength-division-multiplexer, which ensures each of the three Raman Stokes components generated in the long fiber is routed to one FLM and then reflected back with minimum loss. Unlike existing half-open random lasing cavities using fiber Bragg gratings, the reflection bandwidth of FLMs is wide enough to preserve the intrinsic spectral features of each lasing bands, providing a valuable platform to study the mechanism of high-order random lasing in fibers. Also, the reflection efficiency can be treated as an invariant as the pump power grows, significantly reducing the threshold of high-order random lasing. The stationary model is used to calculate the output power, and the results fit the experimental data well.