In this paper we study the approximability of the minimum vertex cover problem in power law graphs. In particular, we investigate the behavior of a standard 2-approximation algorithm together with a simple pre-processing step when the input is a random sample from a generalized random graph model with power law degree distribution. More precisely, if the probability of a vertex of degree i to be present in the graph is , where and c is a normalizing constant, the expected approximation ratio is , where is the Riemann Zeta function of ß, is the polylogarithmic special function of ß and .