To explore the four-alpha-particle condensate state in 16O, we solve a full four-body equation of motion based on the four-alpha-particle orthogonality condition model in a large four-alpha-particle model space spanned by Gaussian basis functions. A full spectrum up to the 0_{6};{+} state is reproduced consistently with the lowest six 0;{+} states of the experimental spectrum. The 0_{6};{+} state is obtained at about 2 MeV above the four-alpha-particle breakup threshold and has a dilute density structure, with a radius of about 5 fm. The state has an appreciably large alpha condensate fraction of 61%, and a large component of alpha+12C(0_{2};{+}) configuration, both features being reliable evidence for this state to be of four-alpha-particle condensate nature.