Until 2004, the owners of MoneyGram were Viad Corp and Travelers Express Company Inc. The benefits of money transfers by MoneyGram: simplicity in making up. The Global Funds Transfer segment is the primary segment of MoneyGram, providing money transfer and bill payment services to consumers, who are often unbanked or underbanked. Today, MoneyGram - is the second world leader by the growth of money transfers between individuals and the dynamics of international network services.