According to the time-domain perturbation wave equation, we derived the mode-coupled equation with the refractive index perturbation in the few-mode fibers. Then, the equation was used to analyze the mode coupling characteristics and their influence on the mode extinction ratio of signals in the case of few-mode fiber connection. Taking a two-mode fiber as an example, we investigated the relationship between the maximum mode coupling efficiency and the connection loss coefficient of perturbative/non-perturbative fibers. It is found that the maximum mode coupling efficiency is about 4 times the connection loss coefficient when the inter-mode coupling is very small. Furthermore, we put forward a formula of mode extinction ratio in the presence of refractive index perturbation in few-mode fibers. The calculation results show that the mode extinction ratio of the signals can be higher than 20 dB when the ratio of the effective phase mismatch factor to the mode coupling coefficient is greater than 10 or the product of mode coupling coefficient and length is less than 0.2.