the "schematic" doesn't show the GND connection of your 12V source.
in another word my LED never turns off !
because the Arduino can never raise the I/O pin higher than its supply voltage - which is of course, 5 V.So if you write it HIGH, the output will go to 5 V, and you will still have 7 V across the LED and resistor.If however, you put three white or four other LEDs in series with the resistor, they will (probably) not turn on at 7 V and you can control them from the I/O pin.As long as the Arduino never loses power while there is any voltage on the 12 V supply.
is there any way to fix it ? (without switching or relay)