In this paper we introduce a length constrained user equilibrium model. In our model, people consider two criteria, path time and path length, when selecting their routes. They only travel on "acceptable paths", the paths whose length are not too long for them. Each user will try to minimize his own path time when he seeking which "acceptable path" to travel. It is shown that this problem can be stated as a convex optimization model, and a column generation algorithm is proposed for its solution. The applications of our model in congestion pricing is also discussed in this paper.