Relativistic ab initio potential curves of RbCs lowest (1,3)Sigma(+) stated are calculated by diagonalizing the Douglas-Kroll-Hess Hamiltonian as implemented in Gaussian09 suite of programs. The ab initio calculations are performed at the CCSD(T) level with UGBS1P+ basis set, a huge all-electron basis set. The rovibrational eigenenergies and eigenfunctions on the lowest (1,3)Sigma(+) ab initio potential curves are calculated by direct diagonalization of molecular Hamiltonian in a Fourier grid discrete variable representation. The results agree well with available experimental and theoretical work and the accuracy of theoretical descriptions of RbCs are increased, which is expected to be a good reference for further investigations.