The company continues to automate and enhance MoneyGram MoneyGram launched a new in-person bill payment service which will be delivered through agents in their domestic network, giving consumers an easy, low-cost method to pay their bills. Until 2004, the owners of MoneyGram were Viad Corp and Travelers Express Company Inc. What are the main benefits of money transfers by MoneyGram? Reliability - the international payment system gives complete assurance that the money will be paid to the recipient. In March 2012, the company MoneyGram merged with the network of U.S. payment centers ZipZap.