A method is presented for the measurement of differential cross-sections of heavy ion elastic scattering induced by Radioactive Ion Beams (RIBs) on the Radioactive Ion Beam Line in Lanzhou (RIBLL) at the Heavy-Ion Research Facility in Lanzhou (HIRFL). The disadvantages of broad beam profiles and limited intensities of the RIBs were overcome using large area detectors, two Parallel-Plate Avalanche Counters (PPACs), two double-sided silicon strip detector (DSSD) telescopes, incorporated with Monte Carlo simulations. The PPACs were used to determine the direction and position of the beam particles. The DSSD telescopes were used to measure scattered particles. Small corrections for the misalignment of detectors and the data normalization were made by assuming the pure Rutherford scattering at very forward angles. The method is suitable for the measurement of the cross-sections on heavy targets at low and intermediate energies, and it has been successfully applied to measure the angular distribution of elastic scattering of Be-7 on Pb target at E-lab = 17.9 MeV/u. (C) 2012 Elsevier B.V. All rights reserved.