The registration of planning fan-beam computed tomography (FBCT) and daily cone-beam CT (CBCT) is a crucial step in adaptive radiation therapy. The current intensity-based registration algorithms, such as Demons, may fail when they are used to register FBCT and CBCT, because the CT numbers in CBCT cannot exactly correspond to the electron densities. In this paper, we investigated the effects of CBCT intensity inaccuracy on the registration accuracy and developed an accurate gradient-based free form deformation algorithm (GFFD). GFFD distinguishes itself from other free form deformable registration algorithms by (a) measuring the similarity using the 3D gradient vector fields to avoid the effect of inconsistent intensities between the two modalities; (b) accommodating image sampling anisotropy using the local polynomial approximation-intersection of confidence intervals (LPA-ICI) algorithm to ensure a smooth and continuous displacement field; and (c) introducing a 'bi-directional' force along with an adaptive force strength adjustment to accelerate the convergence process. It is expected that such a strategy can decrease the effect of the inconsistent intensities between the two modalities, thus improving the registration accuracy and robustness. Moreover, for clinical application, the algorithm was implemented by graphics processing units (GPU) through OpenCL framework. The registration time of the GFFD algorithm for each set of CT data ranges from 8 to 13 s. The applications of on-line adaptive image-guided radiation therapy, including auto-propagation of contours, aperture-optimization and dose volume histogram (DVH) in the course of radiation therapy were also studied by in-house-developed software.