Contact of Iberia airline customer service. Contact Iberia: Find below customer service details of Iberia airline, including phone and address. You can reach the below contact for new flight booking, cancellation, refund, baggage claim, cheap airfares, deals or other queries on Iberia. Besides contact details the page also offers information and links on services of Iberia. Iberia Call Center. 902 400 500 / +34 954 34 99 24.