A memory-programming device includes a voltage generator, a resistive random-access memory, a current detector, and a controller. The voltage generator is configured to generate a program voltage. The resistive random-access memory receives the program voltage to generate a program current. The current detector detects the program current. The controller executes a program procedure. The program procedure includes: gradually ramping up the program voltage by the voltage generator and detecting the program current by the current detector; discovering the maximum of the program current to be a reference current; continuing to ramp up the program voltage by the voltage generator and determining whether the program current detected by the current detector is not less than the reference current; controlling the voltage generator to stop generating the program voltage when the program current is not less than the reference current.