Stabilizer formalism is a powerful framework for understanding a wide class of operations in quantum information. This formalism is a framework where multiple qubit states and sub-spaces are described in a compact way in terms of operators under which they are invariant. In stabilizer formalism, one focuses the members of Pauli groups which have the stabilizing property of a given sub-space. Therefore, finding the Pauli stabilizers of a given sub-space in an efficient way is of great interest. In this paper, this problem is addressed in the field of quantum information theory. We present a two-phase algorithm to solve the problem whose order of complexity is considerably smaller than the common solution. In the first phase, a genetic algorithm is run. The results obtained by this algorithm are the matrices that can potentially be the Pauli stabilizers of the given sub-space. Then an analytical approach is applied to find the correct answers among the results of the first phase. Experimental results show that speed-ups are remarkable as compared to the common solution. © 2014, Springer Science+Business Media New York.