Abstract: The formation and migration of polarons have important influences on physical and chemical properties of transition metal oxides. Density functional theory plus the Hubbard U correction (DFT+U) and constrained density functional theory (cDFT) are often used to obtain the transfer properties for small polarons. In this work we have implemented the cDFT plus the Hubbard U correction method in the projector augmented wave (PAW) framework, and applied it to study polaron transfer in the bulk phases of TiO_2. We have confirmed that the parameter U can have significant impact on theoretical prediction of polaronic properties. It was found that using the Hubbard U calculated by the cDFT method with the same orbital projection as used in DFT+U, one can obtain theoretical prediction of polaronic properties of rutile and anatase phases of TiO_2 in good agreement with experiment. This work indicates that the cDFT+U method with consistently evaluated U is a promising first-principles approach to polaronic properties of transition metal oxides without empirical input.