Daily CTs generated by CBCT correction are required for daily replanning in online-adaptive proton therapy (APT) to effectively deal with inter-fractional changes. Out of the currently available methods, the suitability of a daily CT generation method for proton dose calculation also depends on the anatomical site. We propose an anatomy-preserving virtual CT (APvCT) method as a hybrid method of CBCT correction, which is especially suitable for large anatomy deformations. The accuracy of the hybrid method was assessed by comparison with the corrected CBCT (cCBCT) and virtual CT (vCT) methods in the context of online APT. Seventy-one daily CBCTs of four prostate cancer patients treated with intensity modulated proton therapy (IMPT) were converted to daily CTs using cCBCT, vCT, and the newly proposed APvCT method. In APvCT, planning CT (pCT) were mapped to CBCT geometry using deformable image registration with boundary conditions on controlling regions of interest (ROIs) created with deep learning segmentation on cCBCT. The relative frequency distribution (RFD) of HU, mass density and stopping power ratio (SPR) values were assessed and compared with the pCT. The ROIs in the APvCT and vCT were compared with cCBCT in terms of Dice similarity coefficient (DSC) and mean distance-to-agreement (mDTA). For each patient, a robustly optimized IMPT plan was created on the pCT and subsequent daily adaptive plans on daily CTs. For dose distribution comparison on the same anatomy, the daily adaptive plans on cCBCT and vCT were recalculated on the corresponding APvCT. The dose distributions were compared in terms of isodose volumes and 3D global gamma-index passing rate (GPR) at γ(2%, 2mm) criterion. For all patients, no noticeable difference in RFDs was observed amongst APvCT, vCT, and pCT except in cCBCT, which showed a noticeable difference. The minimum DSC value was 0.96 and 0.39 for contours in APvCT and vCT respectively. The average value of mDTA for APvCT was 0.01cm for clinical target volume and ≤0.01cm for organs at risk, which increased to 0.18cm and ≤0.52cm for vCT. The mean GPR value was 90.9%, 64.5%, and 67.0% for APvCT versus cCBCT, vCT versus cCBCT, and APvCT versus vCT, respectively. When recalculated on APvCT, the adaptive cCBCT and vCT plans resulted in mean GPRs of 89.5±5.1% and 65.9±19.1%, respectively. The mean DSC values for 80.0%, 90.0%, 95.0%, 98.0%, and 100.0% isodose volumes were 0.97, 0.97, 0.97, 0.95, and 0.91 for recalculated cCBCT plans, and 0.89, 0.88, 0.87, 0.85, and 0.81 for recalculated vCT plans. Hausdorff distance for the 100.0% isodose volume in some cases of recalculated cCBCT plans on APvCT exceeded 1.00cm. APvCT contours showed good agreement with reference contours of cCBCT which indicates anatomy preservation in APvCT. A vCT with erroneous anatomy can result in an incorrect adaptive plan. Further, slightly lower values of GPR between the APvCT and cCBCT-based adaptive plans can be explained by the difference in the cCBCT's SPR RFD from the pCT.