A non-rectangular display device comprising: a display unit including: scan lines (S1-SN), data lines (D1-DM), unit areas (512, 522) corresponding to intersections of the scan lines (S1-SN) and the data lines (D1-DM), the unit areas (512, 522) including first unit areas in an effective display area, and second unit areas in a dummy area around the effective display area, some of the second unit areas being smaller than the first unit areas, and pixels in the first unit areas; a timing controller configured to receive first data (Data1) including image data corresponding to the first and second unit areas (512, 522), the timing controller further configured to convert the first data (Data1) into second data (Data2) corresponding to the effective display area, and to output the second data (Data2); and a data driver configured to generate a data signal that corresponds to the second data (Data2), and to supply the data signal to the data lines (D1-DM); wherein the display unit includes a first horizontal line having fewer pixels than the number of the data lines (D1-DM), wherein the data driver is configured to, during a first horizontal period corresponding to the first horizontal line, apply the data signal that corresponds to the second data (Data2) to data lines (D1-DM) connected to the pixels of the first horizontal line, and to apply a predetermined first voltage to the other data lines (D1-DM), wherein the timing controller is further configured to convert the first data (Data1) into second data (Data2) by collectively replacing data corresponding to the second unit areas among the first data (Data1) with digital data (DSx) corresponding to the predetermined first voltage, wherein the first voltage is a lowest voltage of gray level voltages generated by the data driver, characterized in that the timing controller is further configured to transmit, to the data driver, channel information comprising, for each of the horizontal lines included in the display unit, a point at which the effective display area begins and a point at which the effective display area ends. a display unit including: scan lines (S1-SN), data lines (D1-DM), unit areas (512, 522) corresponding to intersections of the scan lines (S1-SN) and the data lines (D1-DM), the unit areas (512, 522) including first unit areas in an effective display area, and second unit areas in a dummy area around the effective display area, some of the second unit areas being smaller than the first unit areas, and pixels in the first unit areas; scan lines (S1-SN), data lines (D1-DM), unit areas (512, 522) corresponding to intersections of the scan lines (S1-SN) and the data lines (D1-DM), the unit areas (512, 522) including first unit areas in an effective display area, and second unit areas in a dummy area around the effective display area, some of the second unit areas being smaller than the first unit areas, and pixels in the first unit areas; a timing controller configured to receive first data (Data1) including image data corresponding to the first and second unit areas (512, 522), the timing controller further configured to convert the first data (Data1) into second data (Data2) corresponding to the effective display area, and to output the second data (Data2); and a data driver configured to generate a data signal that corresponds to the second data (Data2), and to supply the data signal to the data lines (D1-DM); wherein the display unit includes a first horizontal line having fewer pixels than the number of the data lines (D1-DM), wherein the data driver is configured to, during a first horizontal period corresponding to the first horizontal line, apply the data signal that corresponds to the second data (Data2) to data lines (D1-DM) connected to the pixels of the first horizontal line, and to apply a predetermined first voltage to the other data lines (D1-DM), wherein the timing controller is further configured to convert the first data (Data1) into second data (Data2) by collectively replacing data corresponding to the second unit areas among the first data (Data1) with digital data (DSx) corresponding to the predetermined first voltage, wherein the first voltage is a lowest voltage of gray level voltages generated by the data driver, characterized in that the timing controller is further configured to transmit, to the data driver, channel information comprising, for each of the horizontal lines included in the display unit, a point at which the effective display area begins and a point at which the effective display area ends.