Networks are very important in many fields of machine learning research. Within networks research, inferring the structure of unknown networks is often a key problem; e. g. of genetic regulatory networks. However, there are very few well-known biological networks, and good simulation is essential for validating and evaluating novel structural inference techniques. Further, the importance of large, genome-wide structural inference is increasingly recognised, but there does not appear to be a good simulator available for large networks. This paper presents GREENSIM, a simulator that helps address this gap. GREENSIM automatically generates large, genome-size networks with more biologically realistic structural characteristics and 2nd-order non-linear regulatory functions. The simulator itself and the novel method used for generating a network structure with appropriate in-and out-degree distributions may also generalise easily to other types of network. GREENSIM is available online at: http://syntilect.com/cgf/pubs:software