The data signal driving method is disclosed. The method is applied in a display panel. The display panel includes a display region having data lines and a fan-out region having connection lines. The method includes: inputting a reference voltage to each connection lines and obtaining a current in each connection line; setting a most middle connection line as a first connection line, using the first connection line as a reference, respectively calculating and obtaining resistances of a 2nd to a N-th connection lines; inputting a data signal voltage to the connection lines; and inputting a compensation voltage to each of the 2nd to the N-th connection lines according to the data signal voltage and the resistances such that after applying the data signal voltage and the compensation voltages, the current in each connection line is equal; wherein, N is an integer greater than 2. A driving device is also disclosed.