This paper investigates an adaptive consensus problem for distributed scale-free multi-agent systems (SFMASs) by randomly selecting links, where the degree of each node follows a power-law distribution. The randomly selecting links are based on the assumption that every agent decides to select links among its neighbours according to the received data with a certain probability. Accordingly, a novel consensus protocol with the range of the received data is developed, and each node updates its state according to the protocol. By the iterative method and Cauchy inequality, the theoretical analysis shows that all errors among agents converge to zero, and in the meanwhile, several criteria of consensus are obtained. One numerical example shows the reliability of the proposed methods.