We conducted Monte Carlo simulations to investigate the feasibility of the proton beam-range verification with few beam spills before the start of treatment to provide rapid feedback for treatment plan verification and re-planning (if necessary) for improving the accuracy of treatment targeting: a potentially novel intra-treatment image-guided adaptive proton therapy. MCNPX package was used to generate the distributions of positron emitters in a uniform cylinder PMMA phantom irradiated by a collimated 180MeV pristine proton beam. Two PET systems, a small dual-panel rotational PET and a stationary brain PET, with depth-of-interaction (DOI) measurement, were simulated with GATE for imaging. The images were reconstructed with list-mode MLEM algorithm using simulated coincidence data accumulated during- and post-irradiations. Positron activity-ranges were measured as a function of number of beam spills, total acquisition time, crystal cross-section size, crystal length, and the number of coincidence events. Results show that the accuracy of activity-range measurement is a function of data statistics but converging rapidly within few beam spills under simulated conditions; few spills can be sufficient to measure the activity-range within 1.0 mm from the final converged value; the number of spills can be further reduced if acquiring 30-60sec post-irradiation data, which is still considered a rapid intra-treatment imaging. The accuracy and precision of activity-range measurement was also calculated as a function of count statistics under the simulated conditions, providing a general and very useful guideline to calculate the required statistics for an accurate intra-treatment 'in-beam' activity-range measurement.