Given the sparse structure of Ultra Wide-Band (UWB) channels, Compressive Sensing (CS) is exploited for UWB channel estimation. Muti-Task Compressive Sensing (MTCS), as a CS implementation, has exhibited a potential for promoting signal reconstruction. The signal parameters and data sharing can be solved using the Gamma-Gaussian prior. In this paper, the Hierarchy Dirichle processing (HDP) provides the tree structure of the HDP prior for data sharing across multiple tasks. We research the channel estimation performance of HDP Hidden Markov Model based Muti-Task Compressive Sensing (HDP-HMM-MTCS) for UWB communication systems. In particular, investigate the effects of three factors. Firstly, the sparse structure of a standardized IEEE 802.15.4a channel under Line-Of-Sight (LOS) and Non-Line-Of-Sight (NLOS) environments is estimated. Secondly, the CS Rate (CSR) regions' effect on the HDP-HMM-MTCS channel estimation performance is calculated. Thirdly, the SNR regions are compared with the results of the MTCS, Simple-Task Compressive Sensing (STCS), Orthogonal Matching Pursuit (OMP), and the L1 magic estimations. The simulation results demonstrate that the HDP-HMM-MTCS has the minimum executable time and its channel estimation performances exceed those of the MTCS and the other algorithms, regardless of the LOS and NLOS environments. Therefore, the HDP-HMM-MTCS is an effective and efficient UWB channel estimation method for a sparse channel mode.