Let $f$ be a harmonic mapping on the unit disc ${Delta}$ in $mathbb{C}$. We give some condition for $f$ to be a quasiconformal homeomorphism on ${Delta}$ and to have a quasiconformal extension to the whole plane $ar{mathbb{C}}$. We also obtain quasiconformal extension results for starlike harmonic mappings of order ${alpha}{in}(0,1)$.