Let H2 be the Hardy space on the unit disk D={ξ∈C:|ξ|<1}. Suppose u and v are inner functions and at least one of them is nonconstant, the harmonic Hardy space H2u,v is defined by H2u,v=uH2⊕¯v(H2)⊥=uH2⊕¯vzH2. For any x∈H2u,v, define the Toeplitz operator on the H2u,v by ˆTφx=Qu,v(φx), where Qu,v is the orthogonal projection from L2→H2u,v. In this paper, the unitary equivalence of the harmonic Toeplitz operator and the dual truncated Toeplitz operator is obtained, moreover, the sufficient and necessary conditions for when two Toeplitz operators commute is given, and the properties of the harmonic Toeplitz algebra and the commutant of ˆTz are described. Finally, the essential spectrum for the product of finitely many harmonic Toeplitz operators with continuous symbols is obtained in this paper.