Group creativity is affected by both intergroup competition and intragroup competition, but few studies have examined their joint effect. Based on the Motivated Information Processing in Groups (MIP-G) model, the current study aims to explore such joint effects on group idea generation and idea selection. Both intergroup competition (high vs. low) and intragroup competition (competition vs. cooperation) were experimentally manipulated, and 66 three-person groups were randomly assigned to one of the four conditions to perform a brainstorming task. Consistent with our hypotheses, results showed that two types of competitions interacted to determine group idea generation in that groups under the high intergroup competition and intragroup cooperation condition were most creative in terms of fluency and flexibility. Regardless of the level of intergroup competition, groups demonstrated a higher level of idea elaboration under intragroup cooperation but not competition conditions. Moreover, intergroup and intragroup competitions complemented each other in terms of originality in idea generation and idea selection. Specifically, groups under intragroup competition (rather than intragroup cooperation) condition generated and selected ideas of higher originality when the intergroup competition was low; instead, when the intergroup competition was high, the originality of generated or selected ideas was higher for groups under intragroup cooperation condition. We concluded with a discussion of the implications and value of these findings for theoretical research and management practice in organizations.