The company continues to automate and enhance MoneyGram MoneyGram's consumers and agents expect reliability and safety and that is precisely what MoneyGram continues to deliver, transaction by transaction. Until 2004, the owners of MoneyGram were Viad Corp and Travelers Express Company Inc. It is very convenient and quick to transfer money without opening accounts and having no payment cards, precisely due to this wired transfer system MoneyGram has become one of the most common worldwide. The benefits of money transfers by MoneyGram: the opportunity to send a telegram with money transfer (up to 10 words) for free.