Atos, headquartered in France, said too many employees waste time dealing with irrelevant e-mails, according to the Daily Mail.
The company would phase out e-mailing within 18 months, and said it wants people to spend more time talking to each other -- either on the phone or in person.
Atos's 56-year-old chief executive officer Thierry Breton said: "It is not right that some of our fellow employees spend hours in the evening dealing with their e-mails."
Breton said only 20 out of every 200 e-mails received by his staff every day turn out to be important.
"The e-mail is no longer the appropriate tool. It is time to think differently," he said.
He said the main problem was people switching to a "useless" e-mail while they were carrying out a far more important task.
Breton said a real-time messaging interface like that available on Facebook would be preferable to e-mail.