Background: Screening guidelines for women at familial risk of breast cancer without a known causative gene mutation differ internationally. To our knowledge, no randomised controlled MRI-screening trial has been performed. The FaMRIsc-study aims to assess the efficacy of MRI versus mammography screening for familial risk and furthermore assesses the influence of breast density. Methods: In 12 Dutch hospitals, 1355 women aged 30-55 years with a cumulative lifetime risk of ≥20% without a BRCA1/2 mutation were randomised with a web-based computer generated hospital sequence, concealed for participants, physicians and researchers, in either the MRI-group with yearly MRI, clinical breast examination and mammography biennially, or the Mammography-group with yearly mammography and clinical breast examination. Breastfeeding, pregnancy, previous screening and previous ductal carcinoma in situ were permitted, but no previous invasive cancer. Primary outcomes were number, size and nodal-stage of breast cancers. Secondary outcomes were sensitivity, specificity and positive predictive value. Results were also stratified by mammographic density (BI-RADS AD). Intention to screen analyses were performed. This trial was registered with the Netherlands Trial Register, NTR2789. Findings: Between Jan 1 2011, and Dec 31 2017 in the MRI-group (674 women) compared to the Mammographygroup (680 women) with a median follow-up of 5.2 years for both groups, more breast cancers were detected (40 versus 15, p<0•001), invasive cancers were smaller (median size 9 versus 17 mm, p=0•010) and less frequently node positive (4/24, 17% versus 5/8, 63%, p=0•023). In the MRI-group, specificity was significantly lower compared to the Mammography-group (83•8% versus 91•0%, p<0•001), while sensitivity hardly differed (97•5% versus 86.7%, p=0.18). Clinical breast examination contributed hardly to detection (1/55). In incident cancers, tumour stage was better in the MRI-group (p=0•035), with lower numbers of node positive and ≥T2 tumours, while specificity improved in both arms (MRI-group: 87•4%, Mammography-group: 92•6%, p<0•001). All tumours ≥T2 were in the two highest density categories. In BI-RADS density A-C MRI was most effective. Interpretation: The earlier detection by MRI screening and especially the fewer late-stage cancers in incident rounds, may reduce adjuvant chemotherapy and mortality. However, especially for women with the highest breast density at the cost of more false positive results.