The archetypical very-high-energy gamma-ray blazar Mrk 421 was monitored for more than 3 years with the Gas Slit Camera onboard Monitor of All Sky X-ray Image (MAXI), and its longterm X-ray variability was investigated. The MAXI lightcurve in the 3 -- 10 keV range was transformed to the periodogram in the frequency range $f = 1 times 10^{-8}$ -- $2 times 10^{-6}$ Hz. The artifacts on the periodogram, resulting from data gaps in the observed lightcurve, were extensively simulated for variations with a power-law like Power Spectrum Density (PSD). By comparing the observed and simulated periodograms, the PSD index was evaluated as $alpha = 1.60 pm 0.25$. This index is smaller than that obtained in the higher frequency range ($f > 1 times 10^{-5}$ Hz), namely, $alpha = 2.14 pm 0.06$ in the 1998 ASCA observation of the object. The MAXI data impose a lower limit on the PSD break at $f_{rm b} = 5 times 10^{-6}$ Hz, consistent with the break of $f_{rm b} = 9.5 times 10^{-6}$ Hz, suggested from the ASCA data. The low frequency PSD index of Mrk 421 derived with MAXI falls well within the range of the typical value among nearby Seyfert galaxies ($alpha = 1$ -- $2$). The physical implications from these results are briefly discussed.
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