The case came to light recently at Grantham and District Hospital, former workplace of child killer Beverly Allitt.
A statement from Grantham NHS Trust chief executive, Paul Roberts, issued last night, said: "I can confirm that an elderly patient was recently found to have very low blood sugar in circumstances which are unexplained.
"Expert advice indicates that the patient received an inappropriate dose of insulin.
"Hospital managers have carried out an internal inquiry. Security procedures have been stepped up as a precautionary measure. The police in Grantham have been informed and the matter is in their hands."