Strong X-ray flares from the blazar Mrk 421 were detected in 2010 January and February through 7-month monitoring with the MAXI GSC. The maximum 2–10 keV flux in the January and February flares was measured to be 120 ± 10 mCrab and 164 ± 17 mCrab, respectively; the latter is the highest among those reported from the object. A comparison of the MAXI and Swift BAT data suggests a convex X-ray spectrum with an approximated photon index of Γ ≳ 2. This spectrum is consistent with a picture that MAXI is observing near the synchrotron peak frequency. The source exhibited a spectral variation during these flares, slightly different from those in previous observations, in which the positive correlation between the flux and hardness was widely reported. By equating the halving decay timescale in the January flare, tmd ∼ 2.5 × 104 s, to the synchrotron cooling time, the magnetic field was evaluated to be B ∼ 4.5 × 10−2 G (δ/10)−1/3, where δ is the jet beaming factor. Assuming that the light crossing time of the emission region is shorter than the doubling rise time, tmr ≲ 2 × 104 s, the region size was roughly estimated as R < 6 × 1015 cm (δ/10). These results are consistent with values previously reported. For the February flare, the rise time, tmr < 1.3 × 105 s, gives a loose upper limit on the size as R < 4 × 1016 cm (δ/10), although the longer decay time, tmd ∼ 1.4 × 105 s, indicates B ∼ 1.5 × 10−2 G (δ/10)−1/3, which is weaker than the previous results. This could be reconciled by invoking a scenario that this flare is a superposition of unresolved events with a shorter timescale.