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A novel beam-bunching technique has been implemented at a heavy-ion linear accelerator facility by installing a compact two-gap prebuncher and a multilayer beam chopper. A pulsed beam of 2 to 4 MHz, having kinetic energy up to 1.1  MeV/u, is realized by bunching a 2  keV/u continuous beam just upstream of the linac. Around 40% of the continuous beam particles are successively gathered in a single microbunch with a time width of around 15 ns in full width at one-tenth maximum. The number of background beam particles over 250 ns just before the bunched beam is well suppressed to less than 10^{-4} of the number of bunched particles. This technique has been adopted to generate intense α-particle beams for nuclear astrophysics experiments.