Recently, there has been substantial interest in the study of various random networks as mathematical models of complex systems. As these complex systems grow larger, the ability to generate progressively large random networks becomes all the more important. This motivates the need for efficient parallel algorithms for generating such networks. Naive parallelization of the sequential algorithms for generating random networks may not work due to the dependencies among the edges and the possibility of creating duplicate (parallel) edges. In this paper, we present MPI-based distributed memory parallel algorithms for generating random scale-free networks using the preferential-attachment model. Our algorithms scale very well to a large number of processors and provide almost linear speedups. The algorithms can generate scale-free networks with 50 billion edges in 123 seconds using 768 processors.