OpenGL question

I want to put a texture on an .obj such that the alpha region doesn't appear(only want the mapped texture to appear like branches of a tree mapped on a plane).
Here is my code snippet so far:

model1 = glmReadOBJ("object.obj");
glmUnitize(model1);
glmFacetNormals(model1);
glmVertexNormals(model1, 90.0);
glmDraw(model1, GLM_FLAT| GLM_TEXTURE);


Problem is that the area with alpha just appears white. I want it invisible. Only the texture.