A memory driving device and a method thereof applied for a RRAM array are provided. The memory driving device includes a voltage generator, a current detector, and a controller. The voltage generator generates a write voltage. An RRAM cell of the RRAM array is selected according to a selection signal for receiving the program voltage to generate a program current. The current detector detects the program current. The controller executes a driving procedure which includes: obtaining a voltage distribution for the program voltage; determining the initial voltage and the maximum voltage of the program voltage according to the voltage distribution; gradually increasing the program voltage from the initial voltage to the maximum voltage; determining whether the program current exceeds the reference current; and selecting another RRAM cell when the write current exceeds the reference current.