We have been developing a high-energy (1 MeV) pulsed positron beam apparatus employing an RF acceleration method. From the performance tests using an electron beam, a high-energy fine pulse beam (0.5-1 MeV) with a 350 ps period was confirmed to be generated. From the detailed measurements, the large time resolution was shown to be due to the satellite pulses resulting from sub-optimal bunching. Several possibilities to improve bunching characteristics are discussed.