In the radiation therapy of lung cancer, a free-breathing 3D-CT image is usually acquired in the treatment day for image-guided patient setup, by registering with the free-breathing 3D-CT image acquired in the planning day. In this way, the optimal dose plan computed in the planning day can be transferred onto the treatment day for cancer radiotherapy. However, patient setup based on the simple registration of the free-breathing 3D-CT images of the planning and the treatment days may mislead the radiotherapy, since the free-breathing 3D-CT is actually the mixed-phase image, with different slices often acquired from different respiratory phases. Moreover, a 4D-CT that is generally acquired in the planning day for improvement of dose planning is often ignored for guiding patient setup in the treatment day. To overcome these limitations, we present a novel two-step method to reconstruct the 4D-CT from a single free-breathing 3D-CT of the treatment day, by utilizing the 4D-CT model built in the planning day. Specifically, in the first step, we proposed a new spatial-temporal registration algorithm to align all phase images of the 4D-CT acquired in the planning day, for building a 4D-CT model with temporal correspondences established among all respiratory phases. In the second step, we first determine the optimal phase for each slice of the free-breathing (mixed-phase) 3D-CT of the treatment day by comparing with the 4D-CT of the planning day and thus obtain a sequence of partial 3D-CT images for the treatment day, each with only the incomplete image information in certain slices; and then we reconstruct a complete 4D-CT for the treatment day by warping the 4D-CT of the planning day (with complete information) to the sequence of partial 3D-CT images of the treatment day, under the guidance of the 4D-CT model built in the planning day. We have comprehensively evaluated our 4D-CT model building algorithm on a public lung image database, achieving the best registration accuracy over all other state-of-the-art methods. Also, we have validated our proposed 4D-CT reconstruction algorithm on the simulated free-breathing data, obtaining very promising 4D-CT reconstruction results.