The greatest increases in The company installed more than 23,000 new MoneyGram signs around the globe, making it easier for consumers to find MoneyGram agents. Using the MoneyGram system, you can easily send money to your relatives and friends in other countries. MoneyGram Until 2004, the owners of MoneyGram were Viad Corp and Travelers Express Company Inc. Millions of families depend on MoneyGram to safely send money home or pay the bills.