Quantum teleportation faithfully transfers a quantum state between distant nodes in a network, which enables revolutionary information-processing applications. This has motivated a tremendous amount of research activity. However, in the past not a single quantum-teleportation experiment has been realized with independent quantum sources, entanglement distribution prior to the Bell-state measurement (BSM) and feedforward operation simultaneously, even in the laboratory environment. We take the challenge and report the construction of a 30km optical-fibre-based quantum network distributed over a 12.5km area. This network is robust against noise in the real world with active stabilization strategies, which allows us to realize quantum teleportation with all the ingredients simultaneously. Both the quantum-state and process-tomography measurements and an independent statistical hypothesis test confirm the quantum nature of the quantum teleportation over this network. Our experiment marks a critical step towards the realization of a global 'quantum internet' in the real world.