The natural hyperbolic phonon polariton material-orthorhombic molybdenum trioxide (α-MoO₃) has recently attracted much interest , due to the associated ultra-confinement of light and enhanced light-matter interactions. We theoretically propose and study the in-plane anisotropic phonon polaritons (APhPs) in the Kretschmann structure with monolayer and dual layers α-MoO₃. The excitation of phonon polaritons and the corresponding dispersion properties in this multilayer system are studied by using a generalized 4×4 transfer matrix method (TMM). The frequency dispersions with geometrical parameters are also discussed in detail. The results confirm that the interlayer coupling can be modulated by stacking the multilayer films and regulating the thickness of each layer. More interestingly, when the distance between double α-MoO₃ layers is much smaller than the propagation length of PhPs, a strong coupling phenomenon occurs, and the photon tunneling probability and intensity can be greatly improved. When the incident angle is greater than the total internal reflection angle, the phase matching condition for SPhP excitation can be satisfied. Within the 40° incident angle, the SPhP blue-shifts rapidly with the increase of incident angle. But then the dispersion curve no longer changes with increase of incidence angle. The enlargement of the interstitial layer can also lead the Fabry-Perot (FP) resonance mode to be excited. The APhP in layered heterostructure is an important part of today's nanophotonic technology, our study can help optimize and design tunable optoelectronic devices based on hyperbolic materials.