A search for double-beta decays of 136Xe to excited states of 136Ba has been performed with the first phase data set of the KamLAND-Zen experiment. The 0+1, 2+1 and 2+2 transitions of 0{ u}{beta}{beta} decay were evaluated in an exposure of 89.5kg-yr of 136Xe, while the same transitions of 2{ u}{beta}{beta} decay were evaluated in an exposure of 61.8kg-yr. No excess over background was found for all decay modes. The lower half-life limits of the 2+1 state transitions of 0{ u}{beta}{beta} and 2{ u}{beta}{beta} decay were improved to T(0{ u}, 0+ rightarrow 2+) > 2.6times10^25 yr and T(2{ u}, 0+ rightarrow 2+) > 4.6times10^23 yr (90% C.L.), respectively. We report on the first experimental lower half-life limits for the transitions to the 0+1 state of 136Xe for 0{ u}{beta}{beta} and 2{ u}{beta}{beta} decay. They are T (0{ u}, 0+ rightarrow 0+) > 2.4times10^25 yr and T(2{ u}, 0+ rightarrow 0+) > 8.3times10^23 yr (90% C.L.). The transitions to the 2+2 states are also evaluated for the first time to be T(0{ u}, 0+ rightarrow 2+) > 2.6times10^25 yr and T(2{ u}, 0+ rightarrow 2+) > 9.0times10^23 yr (90% C.L.). These results are compared to recent theoretical predictions.
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