Before the execution of the Government Procurement Act, arbitration and litigation are the principal way of the resolution of the public construction. After the execution of the government procurement act, it is to increase a clause to perform contract for mediating dispute (the government procurement act article 85-1 section 2). The government procurement act article 85-1 section 2 was amended in 4th July, 2007 to stipulate: "In the event that the application for mediation referred to in the preceding paragraph is made by the supplier, the entity may not object to such application. When the mediation suggestion or proposal is brought by CRBGP for the construction procurement, referring to disapprove the entity so that they don't come into existence. The application for arbitration referred to in the preceding paragraph is made by the supplier, the entity may not object to such application." It solicited enthusiastically to discuss all of us. Therefore, the characteristic and the settlement way of the public construction dispute, included the type and the classification of the public construction dispute, the settlement way of the public construction dispute, that is to say, many people like to probe into the mediation and arbitration. For this reason, the point of this chapter emphasize the combing of the mediation and arbitration, including to return the cause of the government procurement act, the past history of the amended law, the meaning and the type of the "first Mediation later Arbitration", to tell apart the preceeding of the similar dispute settlement from "first Mediation later Arbitration", the advantage and the defect of the "first Mediation later Arbitration". Furthermore, this chapter will explore to relative problem of the "first Mediation later Arbitration", including application of the practicing law of the "first Mediation later Arbitration" in the public construction, the problem of the concerning of the preceding procedure of the construction arbitration, whether the government procurement act article 85-1 section 2 remount effect or not, whether the government procurement act article 85-1 section 2 is compulsive arbitration or not.