The time-depending formal theory of scattering, initiated by Lippmann and Schwinger is generalized to the case of multi-channel process.Ekstein has attempted to construct such a theory in 1956 and pointed out the orthogonality properties of the set of multi-channel outgoing (incoming) scattering states, which is very important for the establishment of scattering matrix, but it seems to him that the quite general starting point of the L-S formalism is not appreciated. In his work the simplicity of the L-S formalism is lost. He came to the conclusion that the scattering matrix can not be regarded as the matrix of a single linear operator, because he insisted to work in one single interaction representation for all the initial and final states. Thereby the concept of scattering matrix is confused.The present paper deals with the same generalization, but the simplicity of the L-S formalism is preserved. The explicit form of the scattering operator is given. The calculation of the various transition probability in the present case can be made in a similar way as in the original L-S theory.