The trust that runs Maidstone and Tunbridge Wells hospitals has been told it requires improvement, following an inspection.
The Care Quality Commission (CQC) said the Maidstone and Tunbridge Wells NHS Trust had "inadequate" leadership.
However, the quality of care at the trust was rated as "good" with staff found to be "compassionate".
Glenn Douglas, chief executive of the trust, said he took "full responsibility" for leadership issues.
The three-day inspection took place in October.
"We're on a journey and moving forward as an organisation and we're not quite there yet," said Mr Douglas.
"If you look at the report, the leadership is much focused on the governance processes in the organisation and that is where we're concentrating our efforts."
'Quick work needed'
In November, Medway Maritime Hospital, in Kent, was found to be failing to protect patients from "inappropriate or unsafe" care.
And East Kent NHS Trust, which runs hospitals in Canterbury and Margate, has been placed in special measures.
CQC's chief inspector of hospitals, Prof Sir Mike Richards, said: "We saw that quick work was needed to improve the governance of the trust and of a number of the core services we inspected.
"There was a great deal of variation, both in the ability of the senior directorate level management teams to run their services effectively, and in the level of robust clinical oversight of services.
"While the trust acknowledged immediately that these improvements needed to be made when we told them so, we should not have needed to tell them - which highlights how much this work is needed."