In this paper, we propose using a dual-pass composite-ring construction for a stable and wavelength-tunable erbium-doped fiber (EDF) laser with a single-longitudinal-mode (SLM) output. According to the proposed laser architecture, a flattened output power spectrum within a 0.57 dB power variation can be obtained in the tuning range of 1530 to 1560 nm. In addition, the measured optical signal-to-noise ratio (OSNR) of each output wavelength can be larger than 62.1 dB. Furthermore, a stable and tunable dual-wavelength output of the proposed EDF laser scheme can also be achieved in the same operation range by using two optical filters inside a ring cavity. Here, the maximum and minimum mode spacing of dual-wavelength lasing in the proposed EDF laser are 28.01 and 1.04 nm, respectively. In this measurement, the SLM performance and output stability of the proposed EDF laser are analyzed and discussed experimentally.