The application of even and odd coherent states in quantum information is studied. We generate a kind of entanglement with beam splitter by inputting even and odd coherent states into lossless beam splitter. We relate the density operators at the input and output ports of the beam splitter by means of the angular-momentuni transformation and the connection between it's unitary matrix representation and three-dimensional angular-momentum group. Then we get the joint output photo-number distribution. When the vacuum state is injected into one input port while even or οdd coherent state is injected into the other, quantum entanglement is generated at the output ports. Even and odd coherent states have the opposite output quantum entanglement properties in this case. When arbitrary even or οdd coherent states are injected into both of separate input ports, there will be more complicated quantum entanglement at both of output ports.