Wu, G., Liang, K. and Yin, X., 2010. Frequency-domain weighted-averaging finite-difference numerical simulation of qP wave propagation in TTI media. Journal of Seismic Exploration, 19: 207- 229. The finite-difference method is widely used in numerical simulation of the propagation of seismic waves, but has the limitation that numerical dispersion reduces the accuracy and resolution of seismic wavefield simulation. In order to decrease the numerical dispersion of conventional finite-difference operators, this paper presents a frequency-domain weighted-averaging finite-difference operators defined on a 25-point stencil for numerical simulation of qP waves propagating in transversely isotropic media with a tilted symmetry axis (TTI media). We first approximate the differential operators using finite-difference analogues defined on 25-point stencils and then calculate the weighted average of the difference operators with weighting coefficients. The weighting coefficients are determined by the Gauss-Newton method of optimization theory. Using the weighted-averaging finite-difference analogues and combined boundary conditions, we successfully simulate qP wave propagation in homogeneous TTI media, layered TTI media and VTI Salt model. The seismic wavefields in the time and frequency domains are obtained and used to generate single shot records. The result of numerical simulation indicates that 25-point weighted-averaging finite-difference analogues can improve the accuracy of the numerical simulation of wavefields and efficiently suppress the numerical dispersion of conventional difference operators. This method may be employed in the foundation of qP migration and inversion in TTI media.