The reduced subspaces and invariant subspaces of Toeplitz operators are the hot spots of operator theory in recent years. The slant Toeplitz operator is a natural extension of Toeplitz operator. The reduced subspaces of the third order slant Toeplitz operators on unit circle are studied here. By calculating the action of the 3rd order slant Toeplitz operator with zN as the symbol on the canonical basis of Lebesgue Spaces on the unit circle,SN is defined for three kinds of cases where N is mod 3 residue 1, mod 3 residue 2 and mod 3 residue 0, and the division of N is obtained, corresponding to a group of decomposition H (N)j of Lebesgue Spaces. It is proved that for j∈SN,H (N)j are all the minimal subspaces of the 3rd order slant Toeplitz operators with zN sign. The results of reduced subspaces of order 2 slant Toeplitz operators are extended here, which enriches the study of reduced subspaces of slant Toeplitz operators on Lebesgue Spaces, and is of great significance to the study of the structure of slant Toeplitz operators.