We have developed a new analytic method to compute the response of triaxial induction logging tools in layered transverse isotropic (TI) dipping formations without borehole and invasion zones. A triaxial induction tool is composed of one or more sets of three orthogonal transmitter coils and three orthogonal receiver coils arranged along the tool axis. The tool axis may intercept a formation with dip, azimuthal, and rotation angles. Based on the electromagnetic (EM) field in planarly layered media, formulations of the EM fields generated by these three transmitting coils are derived. A fast-forward-modeling algorithm to compute the responses of an induction tool was developed. Compared with the algorithm using the coefficient propagator method previously developed, the proposed algorithm calculates the generalized reflection and transmission coefficients only once for each layer regardless of the position of the transmitters, and therefore, it greatly speeds up the computation. The simulation code solves for all nine components of the magnetic field in a TI layered medium. Results of this new method were developed for several formation models, which agreed very well with the published data. For a dipping or nondipping case in a 28-layer formation, the proposed method was about 37 times faster, which was more appropriate to be used in an inversion algorithm.