We propose a 4D (three spatial dimensions plus time) tissue-volume preserving non-rigid image registration algorithm for pulmonary 4D computed tomography (4DCT) data sets to provide relevant information for radiation therapy and estimate pulmonary ventilation. The sum of squared tissue volume difference (SSTVD) similarity cost takes into account the CT intensity changes of spatially corresponding voxels, which is caused by the variations of fraction of tissue within voxels throughout the respiratory cycle. The proposed 4D SSTVD registration scheme considers the entire dynamic 4D data set simultaneously, using both spatial and temporal information. We employed a uniform 4D cubic B-spline parametrization of the transform and a temporally extended linear elasticity regularization of deformation field to ensure temporal smoothness and thus biological plausibility of estimated deformation. We used a multiresolution multi-grid registration framework with limitedmemory Broyden Fletcher Goldfarb Shanno (L-BFGS) optimization procedure for rapid convergence and limited memory consumption. We conducted experiments using synthetic 2D+t images and clinical 4DCT pulmonary data sets and evaluated accuracy and temporal smoothness of the proposed method via manually annotated landmarks.