Children’s screen time may affect their growth and development. However, differences in the impact of various psychiatric and psychological factors on children’s screen time is a research gap. This study aimed to explore the differences in the influence of related factors affecting children’s screen time based on their sleep, difficulties, and parental control among Japanese elementary and junior high school students. A cross-sectional survey was conducted among parents in Japan. Data on screen time duration, parent–child background, strengths and difficulties, sleep variables, and parental control types were collected from 225 households. A regression analysis revealed that high Strengths and Difficulties Questionnaire (SDQ) scores (β = 0.166, p = 0.008), sleep duration (β = −0.281, p < 0.001), and parental control (β = −0.204, p = 0.001) were significantly related to children’s screen time. Additionally, it was found that parents’ late bedtimes affect children’s screen time by mediating children’s sleep duration. This study, together with previous research, provides comprehensive insights into design interventions to decrease the screen time of children in the Japanese context.