Using Monte Carlo and spin-dynamics methods, we have investigated the dynamic behavior of the classical, antiferromagnetic XY model on a triangular lattice with linear sizes Lр300. The temporal evolutions of spin configurations were obtained by solving numerically the coupled equations of motion for each spin using fourth-order Suzuki-Trotter decompositions of exponential operators. From space-and time-displaced spinspin correlation functions and their space-time Fourier transforms we obtained the dynamic structure factor S(q,w) for momentum q and frequency . Below T KT ͑Kosterlitz-Thouless transition͒, both the in-plane (S xx ) and out-of-plane (S zz ) components of S(q,) exhibit very strong and sharp spin-wave peaks. Well above T KT , S xx and S zz apparently display a central peak, and spin-wave signatures are still seen in S zz . In addition, we also observed an almost dispersionless domain-wall peak at high below T c ͑Ising transition͒, where longrange order appears in the staggered chirality. Above T c , the domain-wall peak disappears for all q. The line shape of these peaks is captured reasonably well by a Lorentzian form. Using a dynamic finite-size scaling theory, we determined the dynamic critical exponent zϭ1.002(3). We found that our results demonstrate the consistency of the dynamic finite-size scaling theory for the characteristic frequency m and the dynamic structure factor S(q,) itself.