Two accretion columns have been argued to form over the surface of a newborn millisecond magnetar for an extremely high accretion rate $gtrsim1.8times10^{-2}M_odot {rm s^{-1}}$ that may occur in the core-collapse of a massive star. In this paper, we investigate the characteristics of these accretion columns and their gravitational wave (GW) radiation. For a typical millisecond magnetar (surface magnetic field strength $Bsim10^{15}$ G and initial spin period $Psim1$ ms), we find (1) its accretion columns are cooled via neutrinos and can reach a height $sim1$ km over the stellar surface; (2) its column-induced characteristic GW strain is comparable to the sensitivities of the next generation ground-based GW detectors within a horizon $sim1$ Mpc; (3) the magnetar can survive only a few tens of seconds; (4) during the survival timescale, the height of the accretion columns increases rapidly to the peak and subsequently decreases slowly; (5) the column mass, characteristic GW strain, and maximum GW luminosity have simultaneous peaks in a similar rise-fall evolution. In addition, we find that the magnetars spin evolution is dominated by the column accretion torque. A possible association with failed supernova is also discussed.
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