Consider a multiplicative group of integers modulo n,denoted by Z(*)(η). Any element α∈ Z(*)(η) is said to be a semi-primitive root if the order of α modulo η is -Φ(η)/2, where -Φ(η) is the Eulerphi-function. In this paper, we classify the multiplicative groups ofintegers having semi-primitive roots and give interesting propertiesof such groups.