Transverse isotropy with a tilted axis of symmetry (TTI) causes image distortion if isotropic models are assumed during data processing. A simple anisotropic migration approach needs long computational times and is sensitive to the signal-to-noise ratio. This paper presents an efficient, general approach to common-depth-point (CDP) mapping to image the subsurface in TTI media from qP-wave seismic data by adding anisotropic and dip parameters to the velocity model. The method consists of three steps: (i) calculating traveltimes and positions of the CDP points; (ii) determining CDP trajectories; (iii) CDP imaging. A crucial step is the rapid computation of traveltimes and raypaths in the TTI media, which is achieved by the Fermat method, specially adapted for anisotropic layered media. The algorithm can image the subsurface of a given model quickly and accurately, and is suitable for application to a bending reflector. The effectiveness of the method is demonstrated by comparing the raypaths, the traveltimes and the results of CDP mapping, when assuming isotropic media, transversely isotropic media with a vertical axis of symmetry (TIV), and TTI media.