With technical advances in radioactive isotope generation, isotopes with positron decay (PDI) become a viable alternative to their stable counterparts for hadron therapy. Due to substantial signal boosting for positron emission tomography (PET), PDI is promising for accurate and precise online beam range (RB) verification. In this study, we quantified the online beam range verification ability of C-11 ion beams for PET imaging. Geant4 was used to simulate the dose and gamma photon distributions inside the phantom generated from C-11 and C-12 ion beams impinging water and PMMA phantoms. Quark Gluon String Pre-compound (QGSP), Binary Ion Cascade (BIC) and High Precision (HP) Neutron model physics-list was used to govern the relevant physics processes for four therapeutic energies (ET ) (to reach the same penetration depth at each energy level for two carbon species). The annihilation gammas (AGs) were determined by a PET system in GATE and the retrace-back method. AG yields with different acquisition times from start of ion history were compared between C-11 and C-12 beams. Exactly after the beam was turned on, AG with time tag ≤ 5 minutes were collected and analyzed. For the water phantom at the lowest ET , the measured AG from C-11 was 8 folds higher than that from C-12 beam, while dropped to 1.09 folds for the highest ET. In general, with the increasing ET , AG yield rates increased for both species. Full width at half maximum (FWHM) of AG distribution peaks were 0.61 mm and 3.3 mm for C-11 at the lowest and highest ET respectively. The results in PMMA were similar to those in water. The simulation results show that C-11 is an excellent candidate for accurate and precise online RB verification using PET.