We report the discovery of bulk superconductivity (SC) at 6.1 K in a quasi-one-dimensional (Q1D) chromium pnictide K2Cr3As3 which contains [(Cr3As3) 2− ]∞ double-walled subnano-tubes with face-sharing Cr 6/2 (As 6/2 ) octahedron linear chains in the inner (outer) wall. The material has a large electronic specific-heat coefficient of 70∼75 mJ K −2 mol −1 , indicating significantly strong electron correlations. Signature of non-Fermi liquid behavior is shown by the linear temperature dependence of resistivity in a broad temperature range from 7 to 300 K. Unconventional SC is preliminarily manifested by the estimated upper critical field exceeding the Pauli limit by a factor of three to four. The title compound represents a rare example that possibly unconventional SC emerges in a Q1D system with strong electron correlations.