A lubricant additive which comprises a succinimide compound or a boronization product thereof is advantageously used for preparation of a lubricant composition which can maintain the property of anti-shudder for a long time without decreasing the transmission torque capacity or the friction coefficient between metals. The succinimide compound is obtained by reacting (a) succinic acid substituted with an alkenyl or alkyl group having 6 to 30 carbon atoms or an anhydride thereof with (b) a polyalkylenepolyamine comprising a polyalkylenepolyamine having a ring structure at an end in an amount of at least 5% by mole of the entire amount of the polyalkylenepolyamine and is represented by following general formula (1): (In the formula, R1 represents an alkenyl or alkyl group having 6 to 30 carbon atoms, m represents an integer of 2 to 4, n represents an integer of 0 to 3, and A represents the ring structure in the polyalkylenepolyamine having a ring structure at an end or a mixed structure comprising the ring structure and an amino group.)