This paper is concerned with leader-following synchronization in a heterogeneous network coupled by a group of heterogeneous LC oscillators. Both the dynamics between the leader and each follower and the dynamics among the followers are nonidentical. A sampled-data-based protocol is proposed. The sufficient criteria for quasi-synchronization are derived based on the delayed input approach and the Lyapunov stability method. Furthermore, the quasi-synchronization error bound can be solved. Finally, simulations are given to illustrate the theoretical results.