We report the results of a search for the B -> Y(4260)K, Y(4260) -> J/psi pi(+)pi thorn p-decays. This study is based on a data sample corresponding to an integrated luminosity of 711 fb(-1), collected at the Upsilon(4S) resonance with the Belle detector at the KEKB asymmetric-energy e(+)e(-) collider. We investigate the J/psi pi(+)pi(-) thorn p-invariant mass distribution in the range 4.0 to 4.6 GeV/c(2) using both B+ -> J/psi pi(+)pi K--(+) and B-0 -> J/psi pi(+)pi K--(S)0 decays. We find excesses of events above the background levels, with significances of 2.1 and 0.9 standard deviations for charged and neutral B -> Y(4260)K decays, respectively, taking into account the systematic uncertainties. These correspond to upper limits on the product of branching fractions, B(B+ -> Y(4260)K+) x B(Y(4260) -> J/psi pi(+)pi(-)) < 1.4 x 10(-5) and B(B-0 -> Y(4260)K-0) x B(Y(4260) -> J/psi pi(+)pi(-)) < 1.7 x 10(-5) at the 90% confidence level.