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In this paper we consider how to determine route traffic flows for traffic assignment problem (TAP). A new approach is proposed for this purpose. It determines the route traffic flows indirectly. It solves the problem based on the solution of the link based model for the user equilibrium TAP given by LeBlanc but without enumerating all routes of the concerned traffic network explicitly. In this approach a modified Frank-Wolfe algorithm is first applied to obtain link traffic flows with different destinations for TAP, which are then used to determine the route traffic flows by a new algorithm. A simple numerical example is given to illustrate the availability of the new approach. A comparison between the new approach and the other algorithms are made.