Add a blending attribute to the model:
http://www.badlogicgames.com/forum/viewtopic.php?f=11&t=10016&p=45952#p45369
Edit.- Link dead. It is like this:
modelInstance.materials.get(0).set(
new BlendingAttribute(GL20.GL_SRC_ALPHA, GL20.GL_ONE_MINUS_SRC_ALPHA)
)