The company continues to automate and enhance MoneyGram The main clients of MoneyGram are students, travelers, immigrants, expatriates, however, recently representatives of businesses who appreciate the advantages of fast and reliable money transfer, joined them. Until 2004, the owners of MoneyGram were Viad Corp and Travelers Express Company Inc. Today the company MoneyGram International - an independent U.S. company, whose shares are traded on the New York Stock Exchange and MoneyGram money transfer is considered one of the largest international money transfer systems without opening a bank account.