This study investigated depression and fear in dual-income parents during the COVID-19 pandemic as predictors of work–family conflict. Using a cross-sectional design, we recruited 214 dual-income parents aged 20 years or older with preschool and primary school children in Korea. Data were collected via an online survey. In the final model for hierarchical regression analysis, the strongest predictor of work–family conflict was depression (β = .43, p < .001), followed by fear (β = .23, p < .001), then weekly working hours (β = .12, p < .05). The final model was statistically significant ( F = 29.80, p < .001), with an explanatory power of 35%. These findings highlight the need to provide dual-income parents with government-led disaster psychological support during COVID-19, such as counseling, education, and mental health management services involving the psychological predictors of work–family conflict. Diverse systematic intervention programs and policy support should also be provided to help them resolve work–family conflict.