Let be a univalent sense-preserving harmonic mapping of the open unit disc D = {z⎜ ⎜z⎜ < 1}. If f satisfies the condition ⎜ω(z)⎜= < k, 0 < k < 1, then is called k-quasiconformal harmonic mapping in D. The main purpose of this paper was to give some properties of the class of k-quasiconformal mappings related to Janowski starlike functions.