The goal is to develop and evaluate a new constrained feature-based cardiac motion estimation (ME) method for cardiac gated (CG) myocardial perfusion (MP) PET images to improve the accuracy of the estimated cardiac motion vector field (MVF). CG-MP PET projection data were generated from the 4D XCAT phantom with realistic anatomical structures and cardiac MVF models, and reconstructed using the STIR simulation and reconstruction software. The interventricular sulcus (IS) was extracted from each CG-MP PET image by applying B-spline extrapolation and interpolation methods to the extracted edges of the left (LV) and right ventricular (RV) walls. The estimated MVFs of the extracted ISs were calculated between adjacent CG frames. In the previously feature-based cardiac ME algorithm, the estimated IS MVF was used as an initial estimate in the conventional optical-flow ME algorithm. The information was found to reduce the aperture problem effect and provide more accurate cardiac MVF estimate as compared to without the information, using the cardiac MVF of the XCAT as the truth. In the new algorithm, it was used as an additional constraint to restrict the range of the search for the cardiac MVF estimate. The new approach was evaluated in terms of accuracy of the estimated cardiac MVF and compared with those using the previous methods. The evaluation results showed the estimated cardiac MVF obtained from using the IS as an initial estimate (S-initial) was more accurate than that using no initial estimate (0-initial) and was comparable to that using the truth MVF as the initial estimate (T-initial). The estimation accuracy was further improved with the S-initial and the IS motion as an additional constraint. In conclusion, we developed and evaluated a new constrained feature-based cardiac ME method for cardiac PET. We demonstrated the new method provided more accurate estimation of the cardiac MVF as compared to the conventional and a previously developed feature-based cardiac ME method for CG-MP PET.