Around the world, MoneyGram is working with leading financial institutions. The company continues to automate and enhance MoneyGram MoneyGram offers an efficient, fast and secure way to send money around the world. Until 2004, the owners of MoneyGram were Viad Corp and Travelers Express Company Inc. The benefits of money transfers by MoneyGram: sender of of transfer can choose to receive a money transfer currency - U.S. dollars or euros.