Using the fiber delayed self-heterodyne method,the short-term frequency stability of the monolithic nonplanar Er∶YAG ring oscillator(NPRO) outputting the single longitudinal-mode was measured. The laser output wavelength is 1645nm. The self-heterodyne beat signal of the laser was achieved under different delay time about 0.25 μs,0.75 μs,1.25 μs,1.75 μs,2.25 μs,2.75 μs,5.25 μs,7.25 μs,9.75 μs,108.5 μs,166 μs. When span of the spectrum analyzer is 20 kHz,sweep time is 10 s,Res BW is 51 Hz and VBW is 1Hz,the 3 dB bandwidth of the beat signal was measured. In the delay time range of 0.25~9.75 μs,through linear fitting of the 3 dB bandwidth under different delay time,the short-term frequency stability of the single longitudinal-mode NPRO laser is 201 Hz/μs. In addition,the 3 dB bandwidth of about 14 kHz was obtained when the lengths of the delay time fiber are about 21.7 km and 33.2 km.