Abstract The action of type IIB superstring in AdS5S5 background given by Metsaev and Tseytlin(MT) can be reformulated in the Nambu-Goto form. For this form we give the new projection operator involving vielbeins in the target space to con-struct local κ-transformations which leave the action invariant. This new formulation of κ-symmetry(called target space form)is first suggested by Schwarz for the Green-Schwarz(GS) model. Due to the difference between GS model and MT model, our con-struction has some new aspects, which is applicable to all models similar to the MT model. An example is given for the AdS5S1 IIB superstring. We also study the κ-symmetry in target space form for the Polyakov model.