It is a matter for debate that which types of dispute may be resolved by arbitration. This problem is concerning the arbitrability of the subject-matter of a dispute. National laws establish the domain of arbitration. Each state decides which matters may or may not be resolved by arbitration in accordance with its own political, social and economic policy. In response to complexity and diversity of a social phenomenon, the dispute also is various, therefore can not be settled efficiently by means of court adjudication to which applies a law strictly. To overcome such problems we are going to seek to make use of arbitration. According to Korean Arbitration Act Art. 3 (1), any dispute in private laws would be the object of arbitral proceedings. For the promotion of fair and free competition, it is increasingly wide-ranging antitrust legislation across the world. It is matter for debate what can an arbitral tribunal do when confronted with an allegation that the contract under which the arbitration is brought is itself an illegal restraint of trade or in some other way a breach of antitrust law. The underlying question is how to accommodate the conflicting congressional policies favoring resolution of private controversies by arbitration and encouraging private suits to protect the public interests served by the antitrust laws. It is necessary to inquire into the arbitrability of antitrust issues on case-by-case basis, because the types of them are quite diverse. If antitrust issues are the dispute in private laws and the contracting parties agreed to submit to arbitration disputes which have arisen or which may arise between them in the antitrust issues, the antitrust disputes are arbitrable. Not only international antitrust disputes but also domestic antitrust disputes are capable of being resolved by arbitration. When the public interests in the enforcement of antitrust legislation are asserted, it is possible to justify the annulment or the refusal of the recognition or the enforcement of an arbitral award that ignores public policy as a matter of it.