Can the President of the United States pardon a non-US citizen for the crime that he/she may have committed in the United States? Or pardoning only works on US citizens.
...He shall have Power to grant Reprieves and Pardons for Offenses against the United States, except in Cases of Impeachment.
The president can grant a pardon for offences against the United States. In other words, he can grant pardons in all federal criminal cases. The nationality of the offender is immaterial.
If a person is convicted of a crime under the laws of the United States, then that person is eligible for a presidential pardon (except in cases of impeachment). It's that simple. This presidential authority comes directly from the US Constitution (see Article II, Section 2, Clause 1), which says nothing about the convicted person's citizenship status.
To clarify the other two answers, what matters isn't the status of the person being pardoned, but the status of the crimes. The President can pardon crimes under federal jurisdiction, what could prevent a pardon for a crime "committed in the United States" would be if someone committed crimes that also/exclusively falls under the jurisdiction of a particular state. In the case of state crimes, pardon powers are usually wielded by governors or boards of paroles, or some combination thereof.
Glancing at Wikipedia's list of people pardoned or granted clemency by a US president reveals several cases of pardons being granted to non-citizens, many quite fascinating. Among them are:
Jean and Pierre Laffitte, along with several other pirates, were charged and/or convicted of piracy, but were pardoned by James Madison due to their service during the War of 1812. The Lafittes were French citizens at the time.
William Lyon Mackenzie, a British citizen, led a revolt in Upper Canada in 1837. As part of these actions, he violated American neutrality laws; he was pardoned for this by Van Buren in 1840.
Servillano Acquino was pardoned by Teddy Roosevelt for his role in the Philippine-American War. The US did have control of the Philippines at the time, but the citizenship status of the people living there at the time is unclear to me. I suspect that they were US nationals rather than citizens (if in fact they had any US status at all.)
Lothar Witzke was a German spy during WWI. He was pardoned by Woodrow Wilson after the war, partly due to his bravery in saving lives after a boiler explosion in prison, and was returned to Germany.
Duncan Renaldo was a Romanian-born actor who was imprisoned for falsely claiming US citizenship and falsifying a passport. He was later pardoned by FDR.