Accurate registration of lung computed tomography (CT) image is a significant task in thorax image analysis. Recently deep learning-based medical image registration methods develop fast and achieve promising performance on accuracy and speed. However, most of them learned the deformation field through intensity similarity but ignored the importance of aligning anatomical landmarks (e.g., the branch points of airway and vessels). Accurate alignment of anatomical landmarks is essential for obtaining anatomically correct registration. In this work, we propose landmark constrained learning with a convolutional neural network (CNN) for lung CT registration. Experimental results of 40 lung 3D CT images show that our method achieves 0.93 in terms of Dice index and 3.54 mm of landmark Euclidean distance on lung CT registration task, which outperforms state-of-the-art methods in registration accuracy.