Ultra-wideband (UWB) technology is a prospective technology for high-rate transmission and accurate localization in the future communication systems. State-of-art channel modeling approaches usually divide the UWB channel into several sub-band channels and model them independently. By considering frequency-dependent channel parameters, a novel analytical UWB channel model with continuous frequency response is proposed. The composite effect of all frequency components within the UWB channel on the channel impulse response (CIR) of delay domain is derived based on the continuous channel transfer function (CTF) of frequency domain. On this basis, a closed-form simulation model for UWB channels and geometry-based parameter calculation method are developed, which can guarantee the continuity of channel characteristics on the frequency domain and greatly reduce the simulation complexity. Finally, the proposed method is applied to generate UWB channel with 2 GHz bandwidth at sub-6GHz and millimeter wave (mmWave) bands, respectively. The channel measurements are also carried out to validate the proposed method. The simulated CIR and power gain are shown to be in good agreement with the measurement data. Moreover, the comparison results of power gain and Doppler power spectral density (DPSD) show that the proposed UWB channel model achieves a good balance between the simulation accuracy and efficiency.