We propose and experimentally investigate a stable and tunable dual-wavelength erbium-doped fiber (EDF) dual-ring laser scheme. Here, two tunable bandpass filters (TBFs) are used inside the dual-ring gain cavity to generate dual-wavelength lasing. And, due to the gain competition of the EDF gain cavity, the mode-spacing (Δλs) of lasing dual-wavelength will be limited at different operating wavelengths. Hence, the minimum and maximum mode-spacing in the proposed EDF laser scheme are 0.75 and 15.35 nm in C-band range. Besides, the output performances of proposed fiber laser have also been studied and analyzed.