Boolean network (BN) is a popular mathematical model for revealing the behavior of a genetic regulatory network, and observability plays a vital role in understanding the underlying network feature. However, the observability of attractor cycles, which is an interesting and important problem, has not been addressed in the literature. In this paper, we first proposed a novel problem on attractor observability in BNs. Identification of the minimum set of consecutive nodes can be used to determine uniquely the attractor cycle from the others in the network. We then develop a linear-time algorithm to identify the desired set of nodes. The proposed approaches are demonstrated and verified by numerical examples. The computational results are given to illustrate both the efficiency and effectiveness of our proposed methods.