We report the observation of the flavor-changing neutral current decay B-->K(*)l(+)l(-) and an im-proved measurement of the decay B-->Kl(+)l(-), where l represents an electron or a muon, with a data sample of 140 fb(-1) accumulated at the Upsilon(4S) resonance with the Belle detector at KEKB. The results for the branching fractions are B(B-->K(*)l(+)l(-))=(11.5(+2.6)(-2.4)+/-0.8+/-0.2)x10(-7) and B(B-->Kl(+)l(-))=(4.8(+1.0)(-0.9)+/-0.3+/-0.1)x10(-7), where the first error is statistical, the second is systematic and the third is from model dependence.