Understanding the underlying architecture of biological networks has been one of the major goals in systems biology and bioinformatics as it can provide insights in disease dynamics and drug development. Such GRNs are characterized by their scale-free degree distributions and existence of network motifs, which are small subgraphs of specific types and appear more abundantly in GRNs than in other randomized networks. In fact, such motifs are considered to be the building blocks of complex networks and they help achieve the underlying robustness demonstrated by most biological networks. The goal of this thesis is to design biological network growing models. As the motif distribution in networks grown using preferential attachment based algorithms do not match that of the GRNs seen in model organisms like E.Coli and yeast,we hypothesize that such models at a single node level may not properly reproduce the observed degree and motif distributions of biological networks. Hence, we propose a new network growing algorithm wherein the idea is to grow the network one motif at a time.The accuracy of our algorithm was evaluated and show better performance than existing network growing models.