In this paper, for K-quasiconformal mappings of a bounded domain into the complex plane, we build a sharp lower bound of Burkholder’s functional. As an application, we give two explicit and sharp lower bounds of Burkholder’s integrals for two subclasses of K-quasiconformal mappings, respectively. As the second application, we obtain a sharp upper bound of the L-integral of (Formula presented.) for certain K-quasiconformal mappings.