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We study the effect of electron interaction in an electronic system with a high-order Van Hove singularity, where the density of states shows a power-law divergence. Owing to scale invariance, we perform a renormalization group (RG) analysis to find a nontrivial metallic behavior where various divergent susceptibilities coexist but no long-range order appears. We term such a metallic state as a supermetal. Our RG analysis reveals noninteracting and interacting fixed points, which draws an analogy to the ϕ^{4} theory. We further present a finite anomalous dimension at the interacting fixed point by a controlled RG analysis, thus establishing an interacting supermetal as a non-Fermi liquid.