Link prediction in complex networks has attracted much attention in recent years and most of work focuses on proposing more accurate prediction algorithms. In fact, “how difficultly the target network can be predicted” can be regarded as an important attribute of the network itself. In this paper it is intended to explain and characterize the link predictability of the network from the perspective of spectrum. By analyzing the characteristic spectrum of the network, we propose the network link predictability index. Through calculating the index, it is possible to learn how difficultly the target network can be predicted before choosing algorithm, and to solve the problem whether the network is unpredictable or the algorithm is inappropriate. The results are useful for the selecting and matching the complex network and link prediction algorithms.