A buncher cavity has been developed for the muons accelerated by a radio-frequency quadrupole linac (RFQ). The buncher cavity is designed for $beta=v/c=0.04$ at an operational frequency of 324 MHz. It employs a double-gap structure operated in the TEM mode for the required effective voltage with compact dimensions, in order to account for the limited space of the experiment. The measured resonant frequency and unloaded quality factor are 323.95 MHz and $3.06times10^3$, respectively. The buncher cavity was successfully operated for longitudinal bunch size measurement of the muons accelerated by the RFQ.
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