A synchrotron-based proton therapy system operates in a low repetition rate pulsed beam delivery mode. Unlike cyclotron-based beam delivery, there is no guarantee that a synchrotron beam can be delivered effectively or precisely under the respiratory-gated mode. To evaluate the performance of gated synchrotron treatment, we simulated proton beam delivery in the synchrotron-based respiratory-gated mode using realistic patient breathing signals. Parameters used in the simulation were respiratory motion traces (70 traces from 24 patients), respiratory gate levels (10%, 20% and 30% duty cycles at the exhalation phase) and synchrotron magnet excitation cycles (T(cyc)) (fixed T(cyc) mode: 2.7, 3.0-6.0 s and each patient breathing cycle, and variable T(cyc) mode). The simulations were computed according to the breathing trace in which the proton beams were delivered. In the shorter fixed T(cyc) (<4 s), most of the proton beams were delivered uniformly to the target during the entire expiration phase of the respiratory cycle. In the longer fixed T(cyc) (>4 s) and the variable T(cyc) mode, the proton beams were not consistently delivered during the end-expiration phase of the respiratory cycle. However we found that the longer and variable T(cyc) operation modes delivered proton beams more precisely during irregular breathing.