The safety syringe assembly is for inserting a needle into a patient and comprises a needle hub assembly and a safety cover. The needle hub assembly includes a needle, needle hub, and hub flex unit. The needle is mounted on the front side of the needle hub while the rear side is for receiving a syringe. The safety cover houses the needle hub assembly in a first position during shipping, a second position during insertion of the needle into the patient, and in a third position after the needle has been inserted into the patient while awaiting disposal. A portion of the safety cover includes magnification enabling a user to view a dosage calibration scale, needle bevel and air bubbles. The hub flex unit assumes a first enlarged position during shipping, is compressed during insertion into the patient, and slides into a third position after usage while awaiting disposal.