This work focused on Nuclear Proliferation and Terrorism: Threat to Global Security. Early efforts at a worldwide non-proliferation drive started in 1953 with the atom for peace programme. But it was not until in 1957, when, in order to forestall the proliferation of nuclear weapons technology by too many states, the United States, Russia (The Soviet Union) and 22 other countries which possessed nuclear energy as well as the technology, signed and ratified the statute which created the International Atomic Energy Agency (IAEA) on July 27^th of that year. This paper examined that terrorists have tried to acquire nuclear weapons or the technology to make one in order to inflict danger on perceived enemies and gain public attention. Focusing on the danger of nuclear weapon proliferation, the paper finds out that efforts at safeguarding and monitoring the use of radioactive materials by the IAEA are inadequate as some radioactive materials are unaccounted for. The paper, thus, argues that the IAEA experiences lack of cooperation by some countries which have refused it access to its nuclear facilities inspection. Also the failure by some countries especially the US and Russia, to fully disarm or eliminate their nuclear weapon stockpiles has inadvertently increased the risk of nuclear proliferation and have encouraged some other countries to develop and stockpile their own weapons for defensive purposes. This paper is historical; hence, it adopts a qualitative method of analysis. Useful piece of information were obtained from important relevant documents, reports and array of secondary sources.