We have grown delta-doped In0.5Ga0.5As /In0.5Al0.5As heterostructures on GaAs substrate applying with InxAl1-xAs compositional graded-step buffers, called metamorphic structures, grown by molecular beam epitaxy. Three types of buffer layers with different compositional gradients and thicknesses have designed to investigate the influence of the strain relaxation process. We characterized the samples by using transmission electron microscopy, triple-axis X-ray diffraction and Hall measurement. Two samples with different compositional gradient show almost same results in electrical properties. On the other hand, it is found that samples with different step thicknesses had shown the large differences in epilayer tilt and mosaic spread in the step-graded buffers. These results indicate that there exists an interrelation between the strain-relaxed buffer and 2DEG transport properties.