OBJECTIVE: To examine perspectives on food access among low-income families participating in a cost-offset community-supported agriculture (CO-CSA) programme. DESIGN: Farm Fresh Foods for Healthy Kids (F3HK) is a multicentre randomized intervention trial assessing the effect of CO-CSA on dietary intake and quality among children from low-income families. Focus groups were conducted at the end of the first CO-CSA season. Participants were interviewed about programme experiences, framed by five dimensions of food access: availability, accessibility, affordability, acceptability and accommodation. Transcribed data were coded on these dimensions plus emergent themes. SETTING: Nine communities in the US states of New York, North Carolina, Washington and Vermont. SUBJECTS: Fifty-three F3HK adults with children. RESULTS: CSA models were structured by partner farms. Produce quantity was abundant; however, availability was enhanced for participants who were able to select their own produce items. Flexible CSA pick-up times and locations made produce pick-up more accessible. Despite being affordable to most, payment timing was a barrier for some. Unfamiliar foods and quick spoilage hindered acceptability through challenging meal planning, despite accommodations that included preparation advice. CONCLUSIONS: Although CO-CSA may facilitate increased access to fruits and vegetables for low-income families, perceptions of positive diet change may be limited by the ability to incorporate share pick-up into regular travel patterns and meal planning. Food waste concerns may be particularly acute for families with constrained resources. Future research should examine whether CO-CSA with flexible logistics and produce self-selection are sustainable for low-income families and CSA farms.