Hi
I'm trying to design a LED driver ( a battery ) using a adaptor how can I improve its life time?

 

Depending on the LED itself.
Most high-powered ones would benefits by using SMPS.

 

Make the LED so dim you can hardly see it for continuous current draw or use pulse width modulation with a variable duty cycle.

 

Sorry! I mean the life time of the battery. Somebody has said " you need to match driver frequency with the LED frequency to improve the battery's life time?" Is he right?
How is it possible?

 

Sorry! I mean the life time of the battery. Somebody has said " you need to match driver frequency with the LED frequency to improve the battery's life time?" Is he right?
How is it possible?

Nope, that's gobbledegook. Hokum. Bull hockey.

A switcher is the best choice: make a current controlled output and the LED will regulate it's own voltage.

Of course, the current level is set to where you are driving the LED.

 

As has been said, use a constant-current output SMPS and run the LED as dim as possible. Both will maximize battery life. PWM without an inductor in the circuit will not significantly lengthen the life of your battery.