Problem of finding the null-space arises in many science and engineering applications. A few of them are bioinformatics, gene expression analysis, structural analysis, computation fluid dynamics, electromagnetics, and optimization theory. Existing methods rely heavily on the structure, size, and sparsity of the matrices in question. Therefore, they are tailored only for particular applications. Many hybrid methods have also been proposed. Instead of being helpful, they turn out to be even more complex. In this paper, we propose a novel method for the computation of null-space using particle swarm optimization. The method does not make any assumptions as such and is even applicable to purely random matrices. In addition, the method is iterative in nature which provides the flexibility of finding an approximate solution whenever a balance is sought between the accuracy and computation time. And yet, despite all this, the method is simple, stable, and has excellent convergence properties.