LetN= (V, A, c, I) be an input network with node setV, arc setA, non-negative arc weight functionscandl. Let σ be the amount of data to be transmitted. The multichannel quickest-path problem is to find a transmission strategy by which the data are partitioned into a set of parts, each of which is sent by a selected routing path inNsuch that the time required to ship σ units of data from the source to the sink is minimal. In this paper a mathematical description of the multichannel quickest-path problem is first given. Then a necessary and sufficient condition for the optimal strategy of the problem is obtained, and a set of formulae of the optimal strategy is derived. Then the multichannel quickest-path problem with capacity constraint is discussed, and a shortest-path first method for the capacity assignment is proposed. Finally, a general algorithm suitable for dynamic network environment with time complexity O(e2+ ne log n) is designed.