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We present the calculation of total cross sections for positron scattering by Rb at intermediate energies by using the coupled-channel optical method, in which an equivalent-local optical potential has been used to describe the continuum and rearrangement process. The present total cross sections are in good agreement with the measurements of Parikh et al. [Phys. Rev. A 47 (1993) 1535] and other theoretical calculation results. Our results show three peaks in the vicinity of 47eV, which have not been found in the previous measurements and theoretical calculations.