We report on the application of poled electro-optic (EO) polymer films in a gap-free, broadband terahertz (THz) system. Using polymer films consisting of 40% Lemke/60% APC (LAPC) as an emitter-sensor pair and a Ti:sapphire regenerative laser pulse amplifier operated at 800-nm-wavelength, we generated and detected transient THz waves, via the optical rectification and EO effect, respectively. We obtained ~12-THz bandwidth from this system with no absorption gaps. The absence of resonant absorption gaps normally seen in THz systems based on crystalline EO materials is attributed to the amorphous form of the polymer films, making our EO polymer emitter-sensor pair advantageous over EO crystals in a gap-free, broadband THz time-domain-spectroscopy (THz-TDS) system. A model has been developed to simulate the spectrum from THz systems and the simulation results were compared with the experimental results. We also report our experiments and simulations for the pulsed THz waves generated by a EO polymer film consisting of 40% DCDHF-6-V/60% APC (DAPC) and detected either by an 80-μm ZnCdTe or a 2-mm ZnTe sensor, with 1300-nm-wavelength pulses from an optical parametric amplifier (OPA). In addition, with the help of our model, we propose employing a wavelength tuning technique to achieve good phase-matching for polymer emitter/sensor pairs, which should lead to very broad bandwidth.