Based on optical galaxy data, we executed a systematic search for galaxy clusters around the 15 steady unidentified EGRET GeV gamma-ray sources in high Galactic-latitude sky (|b| > 30). We found a strong correlation with 3.7σ level between close cluster pairs (merging cluster candidates) and the unidentified EGRET sources, though, in contrast, no correlation with single clusters. This result implies that merging clusters of galaxies are a possible candidate for the origin of high galactic-latitude, steady unidentified EGRET gamma-ray sources.