Humans possess a large amount of, and almost limitless, visual memory, that assists them to remember pictures far better than words. This phenomenon has recently motivated the computer security researchers' in academia and industry to design and develop graphical user identification systems (GUISs). Cognometric GUISs are more memorable than drawmetric GUISs, but takes more time to authenticate. None of the previously proposed GUISs combines the advantages of both cognometric and drawmetric systems. A signature personify a person and a graphical signature is easier to recall than other drawings. This paper proposes a new graphical Signature-based User Identification System named SUIS. It is based on a 2D grid technology, that is used to draw, digitize and store the signature for user identification. SUIS is categorized as both a cognometric and drawmetric system. Unlike other systems that use 2D grid: We take one cell in a grid as one pixel in the drawing; for signature matching, the signature drawn has to follow the same grid cells as the signature stored, independent of the sequence; and that the system is not based on any machine learning model. Increasing the number of grid cells increases the password space, and decreasing the size of the grid cell increases the precision of the signature. These characteristics makes SUIS: (1) Rigorous enough to be a password system, but easy enough to be usable. (2) Independent of the language and device used to draw the signature. (3) Efficient and practical to be used for online authentication systems.