We present a stable and switchable dual-wavelength erbium-doped fiber laser. In the ring cavity, an inverse-Gaussian apodized fiber Bragg grating serves as an ultranarrow dual-wavelength passband filter, a semiconductor optical amplifier biased in the low-gain regime reduces the gain competition of the two wavelengths, and a feedback fiber loop acts as a mode filter to guarantee a stable single-longitudinal-mode operation. Two lasing lines with a wavelength separation of approximately 0.1 nm are obtained experimentally. A microwave signal at 12.51 GHz is demonstrated by beating the dual wavelengths at a photodetector.