  We theoretically study two atoms with $p$-wave interaction in a
one-dimensional waveguide, and investigate how the transverse anisotropy of the
confinement affects the two-body state, especially, the properties of the
resonance. For bound-state solution, we find there are totally three two-body
bound states due to the richness of the orbital magnetic quantum number of
$p$-wave interaction, while only one bound state is supported by $s$-wave
interaction. Two of them become nondegenerate due to the breaking of the
rotation symmetry under transversely anisotropic confinement. For scattering
solution, the effective one-dimensional scattering amplitude and scattering
length are derived. We find the position of the $p$-wave confinement-induced
resonance shifts apparently as the transverse anisotropy increases. In
addition, a two-channel mechanism for confinement-induced resonance in a
one-dimensional waveguide is generalized to $p$-wave interaction, which was
proposed only for $s$-wave interaction before. All our calculations are based
on the parameterization of the $^{40}$K atom experiments, and can be confirmed
in future experiments.
