We investigate the teleparallel dark energy model with purely non-minimal coupling and without potential. We find the analytic solutions of the scalar field in the radiation, matter, and scalar field (or dark energy) dominated eras, respectively. These solutions indicate the tracker behavior in the radiation and matter dominated eras, while the equation of state $w_{\phi}$ of the teleparallel dark energy is determined by the non-minimal coupling constant $\xi$ but insensitive to the initial condition. In the scalar field dominated era, $w_{\phi}$ monotonically decreases and goes to negative infinity at some finite time when $H$ goes to positive infinity, resulting in a future singularity. We also present the possible evolution patterns and the data fittings in this model.