Lightning discharges in Saturn's atmosphere emit radio waves(1) with intensities about 10,000 times stronger than those of their terrestrial counterparts(2). These radio waves are the characteristic features of lightning from thunderstorms on Saturn, which last for days to months(2). Convective storms about 2,000 kilometres in size have been observed in recent years at planetocentric latitude 35 degrees south(3-5) (corresponding to a planetographic latitude of 41 degrees south). Here we report observations of a giant thunderstorm at planetocentric latitude 35 degrees north that reached a latitudinal extension of 10,000 kilometres-comparable in size to a 'Great White Spot'(6,7)-about three weeks after it started in early December 2010. The visible plume consists of high-altitude clouds that overshoot the outermost ammonia cloud layer owing to strong vertical convection, as is typical for thunderstorms. The flash rates of this storm are about an order of magnitude higher than previous ones, and peak rates larger than ten per second were recorded. This main storm developed an elongated eastward tail with additional but weaker storm cells that wrapped around the whole planet by February 2011. Unlike storms on Earth, the total power of this storm is comparable to Saturn's total emitted power. The appearance of such storms in the northern hemisphere could be related to the change of seasons(7), given that Saturn experienced vernal equinox in August 2009.