We construct new conformal minimal 2-spheres of constant curvature linearly full in the quaternion projective space \mathbb{H}{\mathrm{P}}^n by the twistor map \pi :\mathbb{C}{\mathrm{P}}^{\mathrm{2}n+\mathrm{1}}\to \mathbb{H}{\mathrm{P}}^n in a systematic way. That is， we construct 2-spheres linearly full in \mathbb{C}{\mathrm{P}}^{\mathrm{2}n+\mathrm{1}}or \mathbb{C}{\mathrm{P}}^{\mathrm{2}n}satisfying horizontal condition explicitly. （In the latter case， we consider the natural embedding of the map）. We prove all 2-spheres we constructed are non-homogeneous.