The direction of symmetry axis of parallel fracture set in fractured hydrocarbon reservoir affects the transmission of seismic waves markedly, so a medium named fracture-induced TTI (tilted transverse isotropy) double-porosity medium is studied here to discuss the effect of different dip and azimuth angles of a fracture system. Based on the theories of fracture-induced HTI (horizental transverse isotropy) double-porosity medium, the softness and dispersion matrixes of fracture-induced TTI double-porosity medium are derived with the application of Bond transform, and finally, single-order velocity-stress equations are obtained. Furthermore, numerical simulations in xoz plane of 2.5 dimensional vector wavefield are carried out by the method of high-order staggered-grid finite-difference under perfect matched layer (PML) boundary conditions. The results show that the dipand azimuth angles of fractures have great impacts on seismic wave propagation, since the angles can cause the phenomena of shear wave splitting and, in the two-layer model of fracture-induced TTI double-porosity, converted shear wave splitting and shear wave sub-splitting. All of these increase the complexity of seismic wavefield and will lay a foundation of further studies on seismic wave propagation in actual earth layers.