I like SamR 's suggestion, use a LM3914 configured as a bar graph display and drive with a sawtooth waveform.

 

The required LED current is very unclear at this time, but my guess is that it is over 100 mA per stage.

I like the TI part.

ak

 

The required LED current is very unclear at this time, but my guess is that it is over 100 mA per stage.

I like the TI part.

ak

Correct, 300ma

 

Correct, 300ma

None of the suggested IC outputs can supply that amount of current, so they will each need a driver transistor if you go that route.