Background: Recipients of health services value not only convenience but also respectful, kind, and helpful providers. To date, research to improve person-centred HIV treatment has focused on making services easier to access (eg, differentiated service delivery) rather than the interpersonal experience of care. We developed and evaluated a person-centred care (PCC) intervention targeting practices of health-care workers. Methods: Using a stepped-wedge, cluster-randomised design, we randomly allocated 24 HIV clinics stratified by size in Zambia into four groups and introduced a PCC intervention that targeted caring aspects of the behaviour of health-care workers in one group every 6 months. The intervention entailed training and coaching for health-care workers on PCC practices (to capacitate), client experience assessment with feedback to facilities (to create opportunities), and small performance-based incentives (to motivate). In a probability sample of clients who were pre-trained on a client experience exit survey and masked to facility intervention status, we evaluated effects on client experience by use of mean score change and also proportion with poor encounters (ie, score of ≤8 on a 12-point survey instrument). We examined effects on missed visits (ie, >30 days late for next scheduled encounter) in all groups and retention in care at 15 months in group 1 and group 4 by use of electronic health records. We assessed effects on treatment success at 15 months (ie, HIV RNA concentration <400 copies per mL or adjudicated care status) in a prospectively enrolled subset of clients from group 1 and group 4. We estimated treatment effects with mixed-effects logistic regression, adjusting for sex, age, and baseline care status. This trial is registered at the Pan-African Clinical Trials Registry (202101847907585), and is completed. Findings: Between Aug 12, 2019, and Nov 30, 2021, 177 543 unique clients living with HIV made at least one visit to one of the 24 study clinics. The PCC intervention reduced the proportion of poor visits based on exit surveys from 147 (23·3%) of 632 during control periods to 33 (13·3%) of 249 during the first 6 months of intervention, and then to eight (3·5%) of 230 at 6 months or later (adjusted risk difference [aRD] for control vs ≥6 months intervention –16·9 percentage points, 95% CI –24·8 to –8·9). Among all adult scheduled appointments, the PCC intervention reduced the proportion of missed visits from 90 593 (25·3%) of 358 741 during control periods to 40 380 (22·6%) of 178 523 in the first 6 months, and then 52 288 (21·5%) of 243 350 at 6 months or later (aRD for control vs the intervention –4·2 percentage points, 95% CI –4·8 to –3·7). 15-month retention improved from 33 668 (80·2%) of 41 998 in control to 35 959 (83·6%) of 43 005 during intervention (aRD 5·9 percentage points, 95% CI 0·6 to 11·2), with larger effects in clients newly starting treatment (aRD 12·7 percentage points, 1·4 to 23·9). We found no effect on treatment success (based on viral load) in a nested subcohort (379 [83·7%] of 453 in the control phase vs 402 [83·8%] of 480 in the intervention phase; aRD 0·9 percentage points, –5·4 to 7·2). Interpretation: Improving the caring aspects of health-care worker behaviour is feasible in public health settings, enhances client experience, reduces missed appointments, and increases retention.