We study a superminimal surface M immersed into a hyperquadric Q2 in several cases classified by two global defined functions τX and τY,which were introduced by X.X.Jiao and J.Wang to study a minimal immersion f:M → Q2.In case both τX and τY are not identically zero,it is proved that f is superminimal if and only if f is totally real or io f:M → CP3 is also minimal,where i:Q2 → CP3 is the standard inclusion map.In the rest case that τX ≡ 0 or τy ≡ 0,the minimal immersion f is automatically superminimal.As a consequence,all the superminimal two-spheres in Q2 are completely described.