This study aims to reconstruct the correspondence between the lung branch point sets. Here we use the interior point method to develop a new algorithm to solve the point set matching problem. When developing the algorithm we use conjugate gradient inside the inner loop. Also, we use matrix balancing here. To get the numerical results we test our algorithm against several algorithms and we have shown that the proposed algorithm is better than other algorithms. Then we have applied the proposed algorithm to the real data set of match lung branch point sets at FRC/TLC phases.