In this paper the authors classify solvable quadratic complex Lie algebras up to dimension six. Although the classification up to dimension five is known (see e.g. [F. Zhu and Z. Chen, J. Phys. A, Math. Theor. 40, No. 47, 14243–14251 (2007; Zbl 1127.17002)]), in this paper the result is obtained by a different procedure, based principally on the Witt decomposition, the double extension method and properties of graded structures. The three families resulting in dimension six are shown to be non \(i\)-isomorphic, hence non-isomorphic.