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On the basis of first-principles calculations, we show that the M-type hexaferrite BaFe_{12}O_{19} exhibits frustrated antiferroelectricity associated with its trigonal bipyramidal Fe^{3+} sites. The ferroelectric state of BaFe_{12}O_{19}, reachable by applying an external electric field to the antiferroelectric state, can be made stable at room temperature by appropriate element substitution or strain engineering. Thus, M-type hexaferrite, as a new type of multiferoic with coexistence of antiferroelectricity and ferrimagnetism, provides a basis for studying the phenomenon of frustrated antiferroelectricity and realizing multiple-state memory devices.