The establishment of the obligation to resolve a dispute by the arbitrator requires the declaration of his will and acceptance. The acceptance of this obligation by the arbitrator creates a contractual relationship between the arbitrator and the parties to dispute. From the view point of law of obligations this relationship includes some aspects which have been less considered at least in Iranian law due to some legal ambiguities. The present study by answering questions like: whether this contract is in the form of a mutual interest contract or a bare contract, whether an agreement is necessary or the parties can terminate it at any time, whether the contract with the arbitrator is a personal contract or it does not depend on the parties, and finally, whether this contractual relationship is among conditional contracts or a contingent contract, applies the library method to seek an analysis of some aspects of the contract with the arbitrator