We constructed a new three-mode entangled state representation in the three-mode Fock space, which is complete and can make up a new quantum representation. This state can be generated experimentally by combining beamsplitter with polarizer. The entanglement properties are analyzed by obtaining its Schmidt decomposition. As an important application of this state, we consider a single-mode state teleportation by using this new state as a quantum channel, and present the corresponding teleportation scheme.