Agent-based artificial stock markets attracted much attention over the last years, and many models have been proposed. However, among them, few models take into account the social interactions and mimicking behaviour of traders, while the economic literature describes investors on financial markets as influenced by decisions of their peers and explains that this mimicking behaviour has a decisive impact on price dynamics and market stability. In this paper we propose a continuous double auction model of financial market, populated by heterogeneous traders who interact through a social network of influence. Traders use different investment strategies, namely: fundamentalists who make a decisions based on the fundamental value of assets; hybrids who are initially fundamentalists, but switch to a speculative strategy when they detect an uptrend in prices; noise traders who don’t have sufficient information to take rational decisions, and finally mimetic traders who imitate the decisions of their mentors on the interactions network. An experimental design is performed to show the feasibility and utility of the proposed model.