Dicom (Digital Imaging and Communications in Medicine) files stores the personal data of patients in file headers. The personal data of patients can be obtained illegally while archiving and transmitting Dicom files. Therefore, the personal rights of patients can also be invaded. It can be also changed the treatment of disease. This study proposes a new fuzzy logic-based steganography method for the security of medical images. It provides to select randomly the least significant bits (LSB) of image pixels. The message which combined of personal data and comment of doctor, are compressed and encrypted to prevent the attacks.