During image-guided cancer radiation treatment, three-dimensional (3D) tumor volumetric information is important for treatment success. However, it is typically not feasible to image a patient's 3D tumor continuously in real time during treatment due to concern over excessive patient radiation dose. We present a new iterative morphing algorithm to predict the real-time 3D tumor volume based on time-resolved computed tomography (4DCT) acquired before treatment. An offline iterative learning process has been designed to derive a target volumetric deformation function from one breathing phase to another. Real-time volumetric prediction is performed to derive the target 3D volume during treatment delivery. The proposed iterative deformable approach for tumor volume morphing and prediction based on 4DCT is innovative because it makes three major contributions: (1) a novel approach to landmark selection on 3D tumor surfaces using a minimum bounding box; (2) an iterative morphing algorithm to generate the 3D tumor volume using mapped landmarks; and (3) an online tumor volume prediction strategy based on previously trained deformation functions utilizing 4DCT. The experimental performance showed that the maximum morphing deviations are 0.27% and 1.25% for original patient data and artificially generated data, which is promising. This newly developed algorithm and implementation will have important applications for treatment planning, dose calculation and treatment validation in cancer radiation treatment.