In this paper,we introduce the cutoff harmonic Hardy space hn2（T）=H2（T）+{ζ，ζ2，...，ζn}v and study the property of spectra of Toeplitz operator and semi-commutator of two Toeplitz operator act ing on it.We also obtain the spectral inclusiion theorem and necessary and sufficient conditions on that two Toeplitz operators equal one Toeplitz operator,and these conditions are different from the property of Toeplitz,and these conditions are different from the property of Teoplitz operator on classical Hardy space.