Simulation of quantum circuits on classical computers is an important problem in quantum computing. Quantum circuit simulations involve the representation of quantum states that can be viewed as a probability distribution over a very large vector space. Binary Decision Diagrams have been previously used for this purpose. In this work, we use Context-Free-Language Ordered Binary Decision Diagrams for quantum simulations. CFLOBDDs provide exponential compression over BDDs and can be used to efficiently simulate quantum circuits. We observed that CFLOBDDs scale better than BDDs in terms of memory and execution time over BDDs. They also perform better than tensor networks, a widely used quantum simulation technique.