The archetypical very-high-energy gamma-ray blazar Mrk 421 was monitored for more than three years with the Gas Slit Camera on board Monitor of All Sky X-ray Image (MAXI), and its long-term X-ray variability was investigated. The MAXI light curve in the 3-10 keV range was transformed into the periodogram in the frequency range f = 1 x 10(-8)-2 x 10(-6) Hz. The artifacts on the periodogram, resulting from data gaps in the observed light curve, 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 +/- 0.25. This index is smaller than that obtained in the higher-frequency range (f greater than or similar to 1 x 10(-5) Hz), namely, alpha = 2.14 +/- 0.06 in the 1998 ASCA observation of the object. The MAXI data impose a lower limit on the PSD break at f(b) = 5 x 10(-6) Hz, consistent with the break of f(b) = 9.5 x 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 typical values among nearby Seyfert galaxies (alpha = 1-2). The physical implications from these results are briefly discussed.