Acts of terror have impacted on the history of nations, and for that matter the world, from time immemorial. These have led to changes of monarchs, of political leaders, governments and in earlier times even at dynasties. Until recent years, terrorism was considered a foreign trend, something unimaginable on Nigeria soil. Our knowledge of terrorism appeared to have been limited to what we hear and read in the news media about goings-on in places like Pakistan, Afghanistan, Iraq, Iran, Israel etc. However, it is instructive to note that there were sufficient warnings and foreign intelligent report on the infiltration of Islamic extremist into the Northern part of Nigerian with the Al Qaeda Jihadist concept, but all these were ignored. The incessant bombings of Boko Haram and the Umar Farouk Abdul Mutallab attempt to blow up a U.S. Airliner made it expedient for Nigerian to put in place a legislation to address the issue of terrorism in the country. The main focus of the study is on the review of Anti and counter terrorism measures in Nigeria and its impact on Human Right. This study is thereby divided into three major parts, namely: An Over- review of the Nigerian Terrorism (Prevention) Act- 2011, the Nigerian Terrorism (Prevention) Act and Human Right and Recommendations.