Diluted magnetic semiconductors (DMS) [1] are a rapidly growing research field due to their potential applications in spintronic [2] devices. Several semiconducting oxide materials such as CaO [3], ZnO [4], HfO 2 [5], SnO 2 [6], TiO 2 [7] have been shown both experimentally and theoretically to have DMS properties. Normally there exists no magnetism in these material, but it will appear when defects exist. Introducing transition metal substitutions at the cation positions is one way to produce magnetism. Cu atoms in ZnO [4], Fe in SnO 2 [6] were verified to have ferromagnetism and high Curie temperature (T C ). Another way to obtain the high temperature ferromagnetism is doping nonmetal atoms at anion positions, such as the magnetism in N, C doped CaO [8] and C in SrO [9]. Cation intrinsic vacancy also leads to the high T C magnetism -Ca and Hf vacancies in CaO [3] and HfO 2 [5] demonstrate this kind of ferromagnetism origin. As a common wide band semiconductor, TiO 2 has also been studied as a possible DMS material. Both Co doped anatase [7] and rutile [10], and Cr [11] doped anatase TiO 2 have shown high temperature ferromagnetism. And in these transition metal impurity structures, the O vacancy plays a crucial role to ferromagnetism and structure stability [12]. In this letter, we carry out first principle calculations about cation vacancy effect on the ferromagnetism of anatase TiO 2 . Our research shows that like other ionic materials HfO 2 and CaO, the cation vacancy in anatase TiO 2 also induces ferromagnetism.The calculation in this letter is carried out with the GGA [12] exchange correlation in the frame of the full po-tential linear augmented plane wave (FP-LAPW) method using the WIEN2k package [13]. We use a 48-atom supercell in our calculation. With one or two Ti vacancies, the simulated vacancy concentration is 6.25% and 12.5%, respectively. The muffin-tin radius R is chosen to be 1.5 a.u. for the Ti atom and 2.0 a.u. for O atoms. The convergence parameter (RK) max is chosen to be 7.5, where K gives the largest number of the k-vector in the plane wave expansion. This gives well-converged basis sets consisting of approximately 23570 plane waves. Brillouin zone integrations are performed by summations over a 4 × 4 × 3 Monkhorst-Pack [15] special k-point mesh. The calculations are iterated to self-consistency when the total energy change was less than 0.00005 Ry.In anatase, one Ti atom is surrounded by six O atoms, forming a distorted octahedral structure (Fig. 1). The O atoms can be clarified into two classes. We mark them as O1 and O2.According to molecular orbital theory, the 3d and 4s electrons of Ti and the 2p electrons of O form σand π-orbitals, and when the neutral Ti atom is taken from the structure, it will introduce four holes in the molecular orbital. According to the theoretical research of CaO and HfO 2 , the holes will be arranged spin-parallel in the orbital because of Hund's coupling rules and the on-site Coulomb repulsion energy U pp between the holes. Our first principle calculation sh...