By the use of simultaneous fast toroidal and slow poloidal sweeps of a heavy ion beam, plasma potential profiles in the JIPP T-IIU tokamak are measured at the rate of 120 spatial profiles per second. A new method to eliminate the error due to the change of out-of-plane entrance angle caused by large plasma current is successfully applied. One of the key factors is the very homogeneous characteristics of the energy analyser along the wide slit length. A shaped electrode system, instead of guard rings with a resistor chain, successfully increases the homogeneity of the analyser. Error due to the significant change of in-plane entrance angle during a poloidal sweep is carefully minimized and calibrated by a secondary beam ionized by neutral gas introduced in the vacuum vessel. The depth of the measured potential at the plasma centre reaches more than 1.5 keV in ohmic plasmas with an ion temperature of 600 eV. In some cases, a rather wide region of positive potential and a sharp decrease of the potential in the centre of the plasma are observed.