Wigner functions for the eigenstates of k-th power annihilation operators are constructed in phase spaces by using their expressions in Fock presentations. Based on the negativities of their relevant Wigner functions, the non-classical properties of these eigenstates are discussed. The numerical results show that, depending on the complex parameters α, the coherent states are quasi-classical (their Wigner functions are always non-negative), but the eigenstates of k-th (k≥2) power annihilation operators are really non-classical (their relevant Wigner functions can be negative in phase spaces).