A numerical model of a dual-wavelength erbium-doped fiber ring laser is presented based on the Giles' model. According to the gain and loss match condition, the mode competition of dual-wavelength of 1550 nm and 1555 nm is analyzed. Numerical results show that even tiny changes in loss spectrum have great impact on the process of mode competition. Output powers of dual wavelength are equal when loss maches gain. However, random loss perturbation of 0.1 dB will result in the relative output power fluctuations of 1550 nm and 1555 nm up to 9.59% and 9.52%, respectively. One mode is enhanced and the other is eliminated when a long-term loss bias is larger than 0.05 dB.