The benefits of money transfers by MoneyGram: there is no need to open a checking account when implementing the transfer. Money transfers via MoneyGram system can be used as by bank customers, and by people who do not have bank accounts. Since going public two and a half years ago, MoneyGram has made great strides by pouring energy and resources into several critically important areas for business. The company continues to automate and enhance MoneyGram Until 2004, the owners of MoneyGram were Viad Corp and Travelers Express Company Inc. In whatever part of the world you are, you can trust your money transfer to the company MoneyGram.