There were many injustices committed by the US government with regard to Native Americans.
Overall, the major injustice was that the US government constantly removed Native Americans from lands that were theirs (morally, if not legally). This was seen most notably in the Indian Removal from the Southeast US.
Similarly, the US did things like moving Indians onto reservations set up by treaties and then reneging on those treaties. The US government would typically take land promised to Indians away from them whenever it was needed/wanted by white settlers.
The major overall injustice, then, was to take Indians from their land over and over again. This sometimes involved military action, meaning that the government was willing to kill to force Indians to accept being put on the reservations.