Quantum teleportation faithfully transfers a quantum state between distant nodes in a network, enabling revolutionary information processing applications. Here we report teleporting quantum states over a 30 km optical fiber network with the input single photon state and the EPR state prepared independently. By buffering photons in 10 km coiled optical fiber, we perform Bell state measurement after entanglement distribution. With active feed-forward operation, the average quantum state fidelity and quantum process fidelity are measured to be 0.85 and 0.77, exceeding classical limits of 0.67 and 0.5, respectively. The statistical hypothesis test shows that the probability of a classical process to predict an average state fidelity no less than the one observed in our experiment is less than 2.4E-14, confirming the quantum nature of our quantum teleportation experiment. Our experiment marks a critical step towards the realization of quantum internet in the future.