The Marriage and Family Law No. 52/2014/QH13 has become effective since January 1st, 2015. Compared to the Marriage and Family Law No. 22/2000/QH10, this Law has many amendments, additions and new regulations. One of the new regulations is that the statutory of matrimonial property regime is established under their agreement. This agreement has been widely recognisedfor along time in the legal system of many countries such as Japan (Article 755 and Article 756 of the Civil Code), Thailand (Article 1465 of the Civil and Commercial Code), France (Article 1387 of the Civil Code of the France Republic (Law No. 65-570 dated 13.07.1965)), Philippines, ... However, in the Vietnam legal system, matrimonial property regime under their agreement was first defined in the Marriage and Family Law No. 52/2014/QH13. Because this is the new law which has become effective for a short time, the provisions are still general. In this article, the author focuses on analysing and making recommendations of some issues on matrimonial property regime under their agreement as a bas is for its improvement in practice.