The influence of family allergic history on food allergy in offspring in Japan is unknown. We analyzed data from a nationwide birth cohort study using logistic regression models to examine the associations of maternal, paternal, and both parental histories of allergic diseases (food allergy, atopic dermatitis, asthma, and rhinitis) with their child’s food allergy at 1.5 and 3 years of age. This analysis included 69,379 singleton full-term mothers and 37,179 fathers and their children. All parental histories of allergic diseases showed significant positive associations with their child’s food allergy. When both parents had a history of allergic diseases, the adjusted odds ratio (aOR) tended to be higher than when either parent had allergic diseases (p for trend < 0.0001). The highest aOR was detected when both parents had food allergy (2.60; 95% confidential interval, 1.58−4.27), and the aOR was 1.71 when either parent had food allergy (95% confidential interval, 1.54−1.91). The aORs were attenuated but still had significant positive associations after adjusting for the child’s atopic dermatitis, a risk factor for allergy development. In conclusion, all parental allergic diseases were significantly positively associated with their child’s food allergy. The effect of family history showed a stepwise increase in risk from either parent to both parents, and the highest risk of allergic disease was a parental history of food allergy.