The quantum group SLq(2, R) at roots of unity is introduced by means of duality pairings with the quantum algebra U-q(sl(2, R)). Its irreducible representations corresponding to the a type of the quantum algebra are constructed through the universal T-matrix. The irreducible representations corresponding to the A type are also found. An invariant integral on this quantum group is given. Endowed with that some properties like unitarity and orthogonality of the irreducible representations are discussed.