There are a few numbers customers can choose from when attempting to contact Costco customer service. 1  Costco online member services: 1-800-955-2292. 2  General member services: 1-800-774-2678. 3  Costco travel customer service: 1-877-849-2730.  Costco pharmacy: 1-800-607- 1 6861. Business customer service: 1-800-788-9968.