This paper is devoted to the study of Caputo-type fractional FitzHugh-Nagumo equations driven by fractional Brownian motion (fBm). We establish the existence and uniqueness of mild solution under some conditions on the coefficients. The exponential synchronization and finite-time synchronization for the stochastic FitzHugh-Nagumo equations are provided. The analysis of synchronization phenomenon for time-fractional FitzHugh-Nagumo equations perturbed by fBm are provided.