The Ford's Road home, which is run by Edinburgh City Council, was said by a Care Inspectorate report to be weak in care and support, staffing and management and leadership.
The Gilmerton Care Home in the city was also criticised and separately closed to new admissions.
Both closures to new admissions follow a similar course of action at the Pentland Hill Care Home after a string of complaints.
All three homes have made improvements since the inspections that date from May this year but Pentland Hill Care Home is still under investigation by Police Scotland.
Documents on adult social care due to be tabled before councillors next week outline results of visits by the Care Inspectorate watchdog to five council run premises.
Three older people's facilities were ranked in the "good" and "very good" categories - Ferrylee, Silverlea, and Jewel Houses and two other community and support services were described as good.
Ford's Road Home scored lowly, or weak, on most counts including and support and a raft of recommendations were made by inspectors. Gilmerton Road Care Home, run by Four Seasons Healthcare, was said to be weak in three areas including management and leadership in a separate grading process.
Recommendations included that there should be improved participation strategies involving older people and their carers in their care, helping people maintain their independence and better access to garden spaces.
Improvement plans include providing training for staff, identifying "activity champions" within each care home and honing welcome and assurances packs.
Ricky Henderson, Edinburgh council convener of health and wellbeing, said: "There is always room for improvement in some areas and we are addressing these as a matter of priority."
A spokesman for Four Seasons Healthcare said: "We deeply regret that some aspects of the quality of care at Gilmerton Care Home have been below the standards we normally provide.
"The wellbeing of our residents is our priority. We have a comprehensive improvement plan to meet the Care Inspectorate requirements and are working in conjunction with Edinburgh City Council to deliver it. While we focus on these improvements the unit is not accepting new admissions."
Richard Jackson, director of operations, Bupa Care Homes, which runs the Pentland Hill home, said that staff are "committed to putting in whatever resources are needed to sustain these improvements and keep raising standards higher" and the company has implemented changes.
A Care Inspectorate spokesman said: "Most care homes in Scotland perform well, but we do not hesitate to act on concerns. We inspect every home at least once a year, unannounced, but inspect high-risk homes much more frequently.
"We expect every care home to provide high-quality care that meets residents' needs and promotes their rights. Where we have concerns, we do not hesitate to act."