We reported that highly (111)-oriented nanotwinned Cu (nt-Cu) can be grown by DC electroplating using a CuSO4 based electrolyte in our previous study. However, in practical applications, the addition of H2SO4 is required to improve uniformity of the Cu films. In this study, we added H2SO4 in the CuSO4 based electrolyte with different concentrations, ranging from 50 to 110 g/L. It is found that nt-Cu can be fabricated with the addition of the H2SO4 acid at the current densities from 5 A/dm2 to 11 A/dm2. The ratios of (111) to (200) or (111) to (220) X-ray reflections are extremely high, indicating that the (111) preferred orientation is very strong. The texture fraction and texture coefficient could not precisely determine which Cu films contain columnar (111) nt-Cu grains. We propose a criteria to predict the columnar (111) nt-Cu microstructure by the ratios of (111) to (200) and (111) to (220) X-ray reflections. When both ratios exceed 1000, the fabricated Cu films could possess columnar (111) nt-Cu grains.