The equilibrium network flow problem is formulated by adding the link capacity constraints as a mathematical programming, which is capable of describing the realistic traffic assignment problem. The travel cost on any congested link might be expressed in the sum of the running time and the waiting time occurred at the link end. The Lagrange multiplier associated with the link capacity constraint is equivalent to the waiting time of the link. The augmented Lagrange multiplier approach combines the exterior penalty with primal-dual and the Quasi-Newton method with the straight gradient to deal with the capacitated equilibrium network flow problem. The Quasi-Newton method employs the gradient of the objective function to obtain an improving feasible direction scaled by the secondorder derivatives, and makes line search to obtain an optimal step size to guarantee feasibility of either path or link flow