Aqueous solution of sulfuric acid is used as a suitable system to investigate the reactivity of the short-lived radical cation H2O center dot+ which is generated by radiation in water. Ten aqueous solutions containing sulfuric acid with concentration from 1 to 18 mol L-1 are studied by picosecond pulse radiolysis. The absorbance of the secondary radical SO4 center dot- (or HSO4 center dot) formed within the 10 ps electron pulse is measured by a pulse-probe method in the visible range. The analysis of the kinetics show that the radicals of sulfuric acid are formed within the picosecond electron pulse via two parallel mechanisms: direct electron detachment by the electron pulse and oxidation by the radical cation of water H2O center dot+. In highly concentrated solution when SO42- is in contact with H2O center dot+, the electron transfer becomes competitive against proton transfer with another water molecule. Therefore, H2O center dot+ may act as an extremely strong oxidant. The maximum radiolytic yield of scavenged H2O center dot+ is estimated to be 5.3 +/- 0.1 x 10(-7) mol J(-1).