Quantum entanglement swapping is one of the most promising ways to realize the quantum connection among local quantum nodes. In this Letter, we present an experimental demonstration of the entanglement swapping between two independent multipartite entangled states, each of which involves a tripartite Greenberger-Horne-Zeilinger (GHZ) entangled state of an optical field. The entanglement swapping is implemented deterministically by means of a joint measurement on two optical modes coming from the two multipartite entangled states respectively and the classical feedforward of the measurement results. After entanglement swapping the two independent multipartite entangled states are merged into a large entangled state in which all unmeasured quantum modes are entangled. The entanglement swapping between a tripartite GHZ state and an Einstein-Podolsky-Rosen entangled state is also demonstrated and the dependence of the resultant entanglement on transmission loss is investigated. The presented experiment provides a feasible technical reference for constructing more complicated quantum networks.