Consider a multiplicative group of integers modulo n, denoted by $mathbb{Z}_n^*$. Any element $a{in}mathbb{Z}_n^*$ n is said to be a semi-primitive root if the order of a modulo n is $phi$(n)/2, where $phi$(n) is the Euler phi-function. In this paper, we classify the multiplicative groups of integers having semi-primitive roots and give interesting properties of such groups.