In the work, a self-injected erbium-doped fiber (EDF) dual-fiber-ring (DFR) laser configuration for wavelength-adjustable and stable single-longitudinal-mode (SLM) output is experimentally demonstrated. The tuning wavelength bandwidth can be accomplished from 1519.0 to 1588.0 nm covering both C- and L-bands based on the DFR scheme and self-injected loop, when a C-band EDF is exploited as the gain medium. In addition, the output power, laser linewidth and optical signal to noise ratio (OSNR) of the EDF laser are also studied and discussed. Thus, the designed EDF laser not only can narrow the wavelength linewidth for SLM oscillation, but also can broaden the available tuning bandwidth.