Previous studies have suggested that individuals with hypercompetitive attitude and interpersonal insecurity would have a high level of anxiety, and anxiety has been found to strongly impact on sleep quality. However, the associations between competitive attitudes and sleep quality have not been studied until now. The present study aimed to examine whether anxiety mediates the relationship between competitive attitudes and interpersonal relationships with sleep quality. This was a cross-sectional study with a total of 713 college students (age = 20.18 ± 2.16 years old; 78.8% female) recruited online to measure hypercompetitive attitude, personal development competitive attitude, interpersonal security, state anxiety and sleep quality. Path analysis models were conducted in this study. The path analysis models showed that both hypercompetitive attitude and interpersonal security had direct and indirect significant effects on poor sleep quality due to the mediating effect of state anxiety (β = 0.023, 95% bootstrapped CI: 0.005 to 0.047; β = −0.051, 95% bootstrapped CI: −0.099 to −0.010, respectively). However, personal development competitive attitude had only an indirect significant effect, but it had a negative role on poor sleep quality via state anxiety (β = −0.021, 95% bootstrapped CI: −0.042 to −0.008). The current study provided evidence that college students’ competitive attitudes would impact sleep quality and highlighted the mediating role of state anxiety. The current findings suggested that individuals shifting their hypercompetitive thinking to concentrate on ability development would benefit their mental health.