Controllability is one of the most fundamental issues in control theory. This paper focuses on the perturbation analysis for controllability of logical control networks (LCNs) via an algebraic state space representation approach. The function perturbation problem of LCNs is formulated, and the perturbation analysis for controllability of LCNs is divided into four cases based on whether the perturbed control can be replaced. By virtue of the matrix-based method, a kind of controllability perturbation matrix is constructed for each case to reveal the change of controllability matrix of the original LCNs. In addition, a kind of controllability perturbation set is proposed via the graph-based method, which provides a concise resolution for perturbation analysis with respect to controllability. Finally, the obtained results are applied to the reachability of the lactose operon in Escherichia coli.