I try to supply my arduino Nano with a 7.4 v battery.
... but the regulator of the arduino Nano is not very efficient
connect a better regulator ... connect the output of the best regulator on pin 5v and gnd
But I try this two options and both cases I have a current of 60 mA enter in my arduino
60mA isn't too unreasonable.
If you have a 7.4V battery, ALL "linear" regulators (external, or the one on the Nano board) will be approximately equally inefficient. To do better, you have to have a more complex (and probably expensive) "switching regulator", and you'd have to be measuring the current out of the battery, rather than into the arduino. A 90% efficient switching regulator should give you something like 45mA out of the battery while still putting 60mA into the Nano.