The quarterly magazine, which had a print-run of up to 40,000 copies, had been a feature of Upper Class travel for three years. The most recent issue will be the last.
Virgin Atlantic is expected to investigate new customer communication methods.
JBCP has worked with Virgin Atlantic for seven years and will continue to produce its in-flight duty-free and entertainment titles.
Dean Fitzpatrick, managing director of JBCP, commented: 'We were very proud of Carlos. Three years is a relatively long time in customer publishing.'