Teleportation of a general two-mode Gaussian state through double two-mode squeezed state quantum channels is studied. It is found that the quantum channels must be enough entangled for the output state to be inseparable. The required minimum entanglement for the quantum channels to maintain entanglement in the output state depends on the entanglement of the input state when the input state is pure. The minimum entanglement depends not only the on entanglement but also on the global purity of the input state when the input state is mixed.