In the context of economic slowdown and unemployment upsurge in China, many college graduates set their goals on entrepreneurship. To help more new entrepreneurs improve their innovation ability and entrepreneurial success rate, the synergy theory of entrepreneurial psychology and entrepreneurial ability in the entrepreneurial period was put forward from the perspective of cross-cultural adaptation. On the basis of positive psychology, the entrepreneur's psychological quality and innovation ability were combined to help explore the entrepreneur's inner psychology and innovation ability. The study first analyzed the current development status and characteristics of new entrepreneurs through the literature review method, and explored the relationship between cross-cultural adaptation and new ventures. Second, it examined the relationship among achievement incentives, knowledge level, and the role of communication and entrepreneurs' entrepreneurial intentions from the perspective of positive psychology. Finally, based on the influence relationship and personal experience, research hypotheses and models, the study verified the hypotheses by designing questionnaire surveys, and used the controlled variable method to conduct single-factor test analysis on influencing factors and perform a test on the data. The results show that the Cronbach's α coefficient in the QS is 0.894, which has good reliability. According to the regression analysis results, achievement motivation (AM) can significantly affect entrepreneurial intention (EI) (β = 487, < 0.05), knowledge level (KL) and EI (β = 316, < 0.05), and the regression coefficient is greater than 0, but there is no significant effect of communicate effectiveness (CE) on EI ( = 0.109 > 0.05). In the control variables influence analysis, the level of education of new entrepreneurs was negatively correlated with AM. When the college students' educational level improved, their EI decreased. It shows that AM can promote new entrepreneurs to pursue higher goals, and different level of education has a greater impact on entrepreneurs' AM, which has a more significant impact on entrepreneurial intention. The results further prove that entrepreneurs' psychological factors have a particular impact on the development of enterprises.