The preparation of single crystal involves the grain orientation competitive growth. For high melting point metals, Mo is a typical bcc crystal structure and its preferred growth orientation of single crystal was revealed to be the [110] direction, different from the known preferred growth orientation [100] for bcc metals during solidification. This disagreement remains unclear. For the high melting point metal Ir that is a fcc crystal structure, its preferred growth orientation of single crystal remains unknown. Based on electron beam floating zone melting (EBFZM), the orientation competitive growth of these two metals Mo and Ir with three different directions [100], [110] and [111] has been analyzed using solidification theory. It shows that the preferred growth orientation of Mo is the [110] direction at a planar front interface. When introducing the interface energy anisotropy, the preferred growth orientation of Mo could be the [100] or the [110] direction, depending on the magnitude of interface energy anisotropy parameters a₁ and a₂. This result matches well with the experimental results of Mo single crystal prepared by EBFZM. For the fcc structure Ir, its preferred growth orientation always keeps the [100] direction, agreeing with the experimental results of Ir single crystal prepared by EBFZM in this study. Besides, the effects of interface curvature undercooling and kinetic undercooling on the growth behavior of single-crystal metals prepared by EBFZM have been discussed. It demonstrates that when the grain size in the specimen is in the order of about millimeter or less, the curvature undercooling would dominate the grain orientation competitive growth. As the grain size becomes in the order of about centimeter or larger, the kinetic undercooling would prefer the grain competitive growth process.