This is a great question, because, at least here in the States, we see it written almost every way imaginable. Both barbecue and barbeque are accepted spellings, with Bar-B-Que and BBQ being common shortened, abbreviated forms. In England, it's almost always spelled with a C, so barbecue is appropriate. And, if you didn't already know, the word originally comes from the Spanish word barbacoa, which you may have seen in other recipes or at a restaurant. For more on the history and regional differences, see this post at Daily Writing Tips.