Are you sure that both bands of the double are your recombinant protein? One of those bands could be a contaminating protein that co-purifies with your GST-tagged protein.
A western blot, using non-GST antibodies, could provide more insight.
I suspect these two proteins are co-purifying on the basis of similar affinities to your column. I would try adjusting your elution steps to improve the resolution of the fractions. This can be done by lowering the change in elution buffer between each fraction. Hopefully, this will allow you to isolate fractions in which your protein is free from the contaminating protein.