Strong X-ray flares from the blazar Mrk 421 were detected in 2010 January and February through the 7 month monitoring with the MAXI GSC . The maximum 2 – 10 keV flux in the January and February flares was measured as 120 \pm 10 mCrab and 164 \pm 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 \Gamma \gtrsim 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 the 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 , t _ { d } \sim 2.5 \times 10 ^ { 4 } s , to the synchrotron cooling time , the magnetic field was evaluated as B \sim 4.5 \times 10 ^ { -2 } G ( \delta / 10 ) ^ { -1 / 3 } . Assuming that the light crossing time of the emission region is shorter than the doubling rise time , t _ { r } \lesssim 2 \times 10 ^ { 4 } s , the region size was roughly estimated as R < 6 \times 10 ^ { 15 } cm ( \delta / 10 ) . These are consistent with the values previously reported . For the February flare , the rise time , t _ { r } < 1.3 \times 10 ^ { 5 } s , gives a loose upper limit on the size as R < 4 \times 10 ^ { 16 } cm ( \delta / 10 ) , although the longer decay time t _ { d } \sim 1.4 \times 10 ^ { 5 } s , indicates B \sim 1.5 \times 10 ^ { -2 } G ( \delta / 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 . \color black