We observed the TeV blazar 1ES 1218+304 with the X-ray astronomy satellite Suzaku in May 2006. At the beginning of the two-day continuous observation, we detected a large flare in which the 5-10 keV flux changed by a factor of {approx}2 on a timescale of 5 x 10{sup 4} s. During the flare, the increase in the hard X-ray flux clearly lagged behind that observed in the soft X-rays, with the maximum lag of 2.3 x 10{sup 4} s observed between the 0.3?1 keV and 5?10 keV bands. Furthermore we discovered that the temporal profile of the flare clearly changes with energy, being more symmetric at higher energies. From the spectral fitting of multi-wavelength data assuming a one-zone, homogeneous synchrotron self-Compton model, we obtain B {approx} 0.047 G, emission region size R = 3.0 x 10{sup 16} cm for an appropriate beaming with a Doppler factor of {delta} = 20. This value of B is in good agreement with an independent estimate through the model fit to the observed time lag ascribing the energy-dependent variability to differential acceleration timescale of relativistic electrons provided that the gyro-factor {zeta} is 10{sup 5}.