We performed a search for the decay K-L(0) -> 3 gamma with the E391a detector at KEK. In the data accumulated in 2005, no event was observed in the signal region. Based on the assumption of K-L(0) -> 3 gamma proceeding via parity-violation, we obtained the single event sensitivity to be (3.23 +/- 0: 14) x 10(-8), and set an upper limit on the branching ratio to be 7.4 x 10(-8) at the 90% confidence level. This is a factor of 3.2 improvement compared to the previous results. The results of K-L(0) -> 3 gamma proceeding via parity-conservation were also presented in this paper.