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 \gtrsim 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 _ { b } = 5 \times 10 ^ { -6 } Hz , consistent with the break of f _ { 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 .