In this demonstration, we propose and investigate a stable C-band erbium-doped fiber (EDF) laser with compound-ring cavity. To achieve wavelength tunability with single-longitudinal-mode (SML) output, the sub-ring scheme and fiber Bragg grating (FBG) are used inside the ring cavity. Here, different lasing wavelengths can be selected by employing different Bragg wavelengths of FBGs. In this experiment, the obtained optical signal to noise ratios (OSNRs) and output powers are larger than 44.5 dB and 8.0 dBm respectively in the tuning range of 1531.70-1547.88 nm. Moreover, the output wavelength and power fluctuations of the proposed EDF laser are less than 0.02 nm and 0.1 dB in an observation time of 30 min, respectively.