Biological systems are often composed of various heterogeneous units. It is an important problem to investigate how this heterogeneity affects the network dynamics, namely synchronization phenomenon. We study the heterogeneous networks of FitzHugh–Nagumo oscillators with diffusive coupling and present sufficient conditions for synchronization in these networks using the Lyapunov functions and Linear Matrix Inequalities (LMIs). Starting consideration with the case of two coupled systems further we extend the results to the networks with greater number of nodes. Numerical examples are presented to illustrate the obtained results.