A tire inner liner having a rubber composition based on at least one butyl rubber, a reinforcing filler, graphite and a plasticizing system. The plasticizing system comprises a hydrocarbon plasticizing resin, the glass transition temperature Tg of which is above 20° C. and the softening point of which is below 170° C. A process for producing such a composition for a tire inner liner comprises incorporating into a diene elastomer, in a mixer: a reinforcing filler, graphite, and a plasticizing system, by thermomechanically mixing all the ingredients, one or more times, until a maximum temperature between 110° C. and 190° C. is reached; cooling the mixture down to a temperature below 100° C.; then incorporating a crosslinking system; and mixing everything until a maximum temperature below 110° C. is reached.