The pressure induced phase transitions of TiO2 from anatase to columbite structure and from rutile to columbite structure and the temperature induced phase transition from anatase to rutile structure and from columbite to rutile structure are investigated by ab initio plane-wave pseudopotential density functional theory method (DFT), together with quasi-harmonic Debye model. It is found that the zero-temperature transition pressures from anatase to columbite and from rutile to columbite are 4.55 GPa and 19.92 GPa, respectively. The zero-pressure transition temperatures from anatase to rutile and from columbite to rutile are 950 K and 1500 K, respectively. Our results are consistent with the available experimental data and other theoretical results. Moreover, the dependence of the normalized primitive cell volume V/V0 on pressure and the dependences of thermal expansion coefficient α on temperature and pressure are also obtained successfully.