We predicted peculiar ghost surface phonon polaritons in biaxially hyperbolic materials, where the two hyperbolic principal axes lie in the plane of propagation. We took the biaxially-hyperbolic α-MoO3 as one example of the materials to numerically simulate the ghost surface phonon polaritons. We found three unique ghost surface polaritons to appear in three enclosed wavenumber-frequency regions, respectively. These ghost surface phonon polaritons have different features from the surface phonon polaritons found previously, i.e., they are some hybrid-polarization surface waves composed of two coherent evanescent branch-waves in the α-MoO3 crystal. The interference of branch-waves leads to that their Poynting vector and electromagnetic fields both exhibit the oscillation-attenuation behavior along the surface normal, or a series of rapidly attenuated fringes. We found that the in-plane hyperbolic anisotropy and low-symmetric geometry of surface are the two necessary conditions for the existence of these ghost surface polaritons.