This paper proposes a sampling strategy for bandlimited graph signals over perturbed graph, in which we assume the edge between any pair of the nodes may be deleted randomly. Considering the mismatch between the true graph and the presumed graph, we derive the mean square error (MSE) of the reconstructed bandlimited graph signals. To minimize the MSE, we propose a greedy-based algorithm to obtain the optimal sampling set. Furthermore, we use Neumann series to avoid the pseudo-inverse computing. An efficient algorithm with low-complexity is thus proposed. Finally, numerical results show the superiority of our proposed algorithms over the other existing algorithms.