Purpose: In order to learn more about the antecedents of strategy at the top management team’s (TMT) level, the purpose of this paper is to investigate the effects of TMT cultural intelligence on corporate entrepreneurship strategy. Then, the authors examine how TMT’s ambiguity tolerance mediates this relationship. Design/methodology/approach: The authors tested the hypothesis by collecting survey data from 41 TMTs of small- and medium-sized enterprises in the south-east of Iran. Findings: The survey results confirm that a high level of cultural intelligence in TMTs is conducive to corporate entrepreneurship. Furthermore, the result shows that higher levels of cultural intelligence in TMTs relate to a higher level of ambiguity tolerance, which, in turn, enhances the possibility of pursuing corporate entrepreneurship strategy by SMEs. Research limitations/implications: The data for this study were obtained from 41 TMTs in the south-east of Iran, which increases the probability that the results may not be directly transferable to certain companies in Western countries. Future research might attempt to test the ideas developed in this paper across different settings and samples. Originality/value: Several theoretical and empirical studies have explored possible antecedents of corporate entrepreneurship. But a few papers investigated the role of TMT dispositions on corporate entrepreneurship strategy. By addressing the prominent role of TMT psychological dispositions on corporate entrepreneurship strategy, this paper attempts to fill this gap.