Comments on the circuit as hand-drawn in the original posting:
1. You have no current limit on the LED, nor on the base-emitter diode of your drive transistor. Remember that the op-amp output is a relatively low-impedance voltage output, so when it is high, it is able to source fairly high currents (see the data sheet for details). The output of the op-amp is connected through the base-emitter diode to the LED. You have a resistor on the collector of your drive transistor, but nothing to limit the current going from op-amp to base to emitter to LED. You don't say what kind of op amp you're using -- maybe the output won't mind this, but maybe it will. A suitable resistor between the op amp output and the transistor base will make sure you don't stress the op amp output, and will help you avoid blowing out the LED or drive transistor.
2. Remember one of the basic rules of op-amps, no current goes in our out of the inputs (this isn't strictly true, but it's a close approximation to the truth). So your two paralleled resistors on the + input have no current going through them, thus no voltage across them, so they're not doing anything useful. You can replace them with a wire directly connecting the voltage divider to the + input, without changing the behavior of your circuit significantly. Others have pointed this out.
I see in your latest post you say you've connected the inverting input to ground through a resistor, but again, there's no reason for the resistor, since no significant current will flow through it, so no voltage will appear across it. If you connect the inverting input to ground, then the output of the op amp will be high any time the non-inverting input has any voltage above ground. Is that what you want?
3. As has been pointed out, you've drawn it so that it will light up when the battery voltage is less than the output of the voltage divider. If you want it to light up when the battery is high instead of low, then swap the + and - inputs.
4. Dave said it was possible to use an op amp as a comparator, but he didn't claim it was a great idea. Some op amps aren't necessarily designed to work well when the inputs are at radically different voltages and the output is being driven hard to one end or the other.