A large proportion of the global burden of childhood cancer arises in China. These patients have a poor quality of life (QoL) and their family caregivers have high unmet needs. This paper examined the association between the unmet needs of family caregivers and the care recipient’s QoL. A total of 286 childhood cancer caregivers were included in this cross-sectional study. Unmet needs and depression among caregivers were assessed by the Comprehensive Needs Assessment Tool for Cancer Caregivers (CNAT-C) and the Patient Health Questionnaire (PHQ-9), respectively. The patient’s QoL was proxy-reported by the Pediatric Quality of Life Inventory Measurement Models (PedsQL 3.0 scale Cancer Module). Descriptive analyses, independent Student’s t-tests, one-way ANOVA, and mediation analyses were performed. The mean scores (standard deviations) for unmet needs, depression, and QoL were 65.47 (26.24), 9.87 (7.26), and 60.13 (22.12), respectively. A caregiver’s unmet needs (r = −0.272, p < 0.001) and depression (r = −0.279, p < 0.001) were negatively related to a care recipient’s QoL. Depression among caregivers played a mediating role in the relationship between a caregiver’s unmet needs and a care recipient’s QoL. As nursing interventions address depression among caregivers, it is important to standardize the programs that offer psychological support to caregivers.