Accurate estimation of fracture density and orientation is of great significance for seismic characterization of fractured reservoirs. Here, we propose a novel methodology to estimate fracture density and orientation from azimuthal elastic impedance (AEI) difference using singular value decomposition (SVD). Based on Hudson's model, we first derive the AEI equation containing fracture density in HTI media, and then obtain basis functions and singular values from the normalized AEI difference utilizing SVD. Analysis shows that the basis function changing with azimuth is related to fracture orientation, fracture density is the linearly weighted sum of singular values, and the first singular value contributes the most to fracture density. Thus, we develop an SVD-based fracture density and orientation inversion approach constrained by smooth prior elastic parameters. Synthetic example shows that fracture density and orientation can be stably estimated, and the correlation coefficient between the true value and the estimated fracture density is above 0.85 even when an S/N ratio of 2. Field data example shows that the estimated fracture orientation is consistent with the interpretation of image log data, and the estimated fracture density reliably indicates fractured gas-bearing reservoir, which could help to guide the exploration and development of fractured reservoirs.