We present an improved measurement of CP-violating asymmetries in B-0-->pi(+)pi(-) decays based on a 78 fb(-1) data sample collected at the Y(4S) resonance with the Belle detector at the KEKB asymmetric-energy e(+)e(-) collider. We reconstruct one neutral B meson as a B-0-->pi(+)pi(-) CP eigenstate and identify the flavor of the accompanying B meson from inclusive properties of its decay products. We apply an unbinned maximum likelihood fit to the distribution of the time intervals between the two B meson decay points. The fit yields the CP-violating asymmetry amplitudes A(pipi) = +0.77 +/-0.27(stat) +/-0.08(syst) and S-pipi = -1.23+/-0.41(stat) (+0.08)(-0.07)(syst), where the statistical uncertainties are determined from the Monte Carlo pseudoexperiments. We obtain confidence intervals for CP-violating asymmetry parameters A(pipi) and S-pipi based on a frequentist approach. We rule out the CP-conserving case, A(pipi) = S-pipi = 0, at the 99.93% confidence level. We discuss how these results constrain the value of the Cabibbo-Kobayashi-Maskawa (CKM) angle phi(2).