The irregular structure of a 3D point cloud, which is composed of the 3D coordinates of irregularly sampled points, poses great challenges to its sparse representation. In this letter, by taking advantage of the permutation-invariant characteristic, we propose a novel method for sparsely representing 3D point clouds, namely permuted sparse representation (PSR). Specifically, we permute the points of a 3D point cloud for increasing its regularity to adapt to a predefined transform, e.g., discrete cosine/wavelet transform. More precisely, the permutation is directly driven by optimizing the objective of sparse representation. Our PSR is elegantly and explicitly formulated as a constrained optimization problem, and an efficient algorithm is proposed to solve it iteratively with the convergence guaranteed. Experimental results demonstrate the advantage of our PSR over the existing ones, i.e., with the same approximation error, the number of non-zero coefficients by our method is only 30% of that of the existing method.