The problem of link disjoint paths pair with QoS constraints was discussed.Two routing models about link dis-joint optimal paths pair with QoS constraints were constructed.First it proved that the problem of link disjoint paths pair in the undirected graph without end to end QoS constraints counld be converted to the correspond problem in its link split graph

while the problem with end to end QoS constraints counld not be converted.Then it’s proved that both of these questions are NP complete.Finally the approximation algorithms is given and simulation on them is made.