Is it possible to use LCD (the 16 pins) without potentiometer?
Sure. You can use two resistors in series to be a "fixed value" potentiometer.

The "wiper" of the potentiometer is the junction between the two resistors. 

I can't tell you what values to use, so you'll have to experiment. You want them to add up to somewhere in the tens of kilo-ohms though, ideally, though the value isn't that critical - it's the ratio between the two values that is of interest, and it's that which gives you your contrast setting.