Positron emission tomography (PET) imaging has been adopted clinically to verify proton beam range (BR) in proton therapy. Conventional approaches use off-line verification that verifies BR after delivery of full dose of a treatment fraction. This verification can be used to check the accuracy of current therapy retrospectively, but its effect suffers from potential target deviation between treatment fractions. In contrast, on-line verification can verify BR using a low dose proton beam and a short data acquisition time prior to administration of a treatment fraction. It could provide adequate information to verify or even revise the beam delivery for improving therapy targeting within a single treatment fraction. Nevertheless, a practical on-line verification has many unknowns and technical challenges. This thesis studies the feasibility of on-line BR verification with PET imaging from three aspects. First, it investigates the impact of count statistics on the accuracy and precision of BR verification. In general, on-line verification is hampered by low count statistics that degrade PET images and subsequently the accuracy and precision of BR verification. We used Monte Carlo simulation to understand the quantitative relationship between count statistics and the accuracy and precision of BR verification under various proton irradiation and PET imaging conditions. A mathematical model was also developed to study the impact of Poisson noise associated with PET images on BR verification. Second, it evaluates the effectiveness of existing algorithms and develops new approaches for improving the accuracy and precision of on-line BR verification. Important factors were identified, effective and efficient approaches were developed. By optimizing and applying these factors and approaches, it is feasible to substantially improve the accuracy and precision of on-line BR verification with the same proton dose and negligible extra processing time. Lastly, it investigates the feasibility of achieving on-line BR verification for proton brain therapy with Monte Carlo simulation, and proposes a new PET system configuration for on-line verification. It demonstrates that by using proper data correction and advanced algorithms, it is feasible to achieve 1-mm accuracy and precision of on-line BR verification with low proton dose and short data acquisition under different proton irradiation conditions.