Objective The skeleton is not good at the neutral and not the simplest by the algorithm using the double distance field. An efficient 3-D thinning algorithm was proposed based on topological invariance to extract the skeleton of the pulmonary trachea in this paper. Methods Firstly this paper introduces the two algorithms basic on double distance field and topological invariance. Then through the proof of Euler characteristic invariant, the algorithm calculates the Euler value by using the Euler look-up table (LUT) and computes the connectivity of 26-connected neighbors. The algorithm uses the Euler value and connectivity to ensure topological invariance. Through the definition of simple point with the constant geometric properties and parallel refinement strategy, the algorithm quickly accesses to a single pixel wide and connected skeleton center-line. Results This algorithm can be applied to the pulmonary trachea quickly to extract the skeleton. Conclusions This algorithm achieves better results compared to the skeleton extraction algorithm based on distance field: the skeleton is located near the airway center-line and is connected, smooth, and single pixel wide. The algorithm is robust and not sensitive to noise.