Metal hole arrays (MHAs) slab is an important component for understanding the mechanism of various surface waves in the terahertz regime, such as spoof surface plasmon, localized surface wave, etc. We have fundamentally researched the resonant properties of surface waves on MHAs slab by asymmetrical incident waves. The resonant mode splitting phenomenon observed in the study, shows that there was a strong coupling between the in-plane wave and the surface wave vector of the MHAs, which is different from strong near field coupling induced modes splitting in terahertz metamaterial systems. We also found the resonant modes that are lower and higher than the cutoff frequency, exhibited different attenuate behaviors. Our research reveals the fact that although the physical mechanisms of modes splitting in MHAs and metamaterial systems are different, both of these effects are due to the break of symmetry in broad sense. All these theoretical and experimental studies are helpful for the design of terahertz components.