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 ontainer hidden">, ontainer hidden"> and ontainer hidden"> transitions of 0νββontainer hidden"> decay were evaluated in an exposure of ontainer hidden"> of 136Xe, while the same transitions of 2νββontainer hidden"> decay were evaluated in an exposure of e05e261d4e72ae276048dd21e7785bc">ontainer hidden">. No excess over background was found for all decay modes. The lower half-life limits of the ontainer hidden"> state transitions of 0νββontainer hidden"> and 2νββontainer hidden"> decay were improved to ontainer hidden"> and ontainer hidden"> (90% C.L.), respectively. We report on the first experimental lower half-life limits for the transitions to the ontainer hidden"> state of 136Xe for 0νββontainer hidden"> and 2νββontainer hidden"> decay. They are ontainer hidden"> and ontainer hidden"> (90% C.L.). The transitions to the ontainer hidden"> states are also evaluated for the first time to be ontainer hidden"> and ontainer hidden"> (90% C.L.). These results are compared to recent theoretical predictions.