Reconstructing the topological structure of biological regulatory networks from microarray expression data or data of protein expression profiles is one of major tasks in systems biology. In recent years, various mathematical methods have been developed to meet this task. Here, based on our previously reported reverse engineering method, we propose a new constraint, i.e., the minimum network constraint, to facilitate the reconstruction of biological networks. Three well studied regulatory networks (the budding yeast cell cycle network, the fission yeast cell cycle network, and the SOS network of Escherichia coli) were used as the test sets to verify the performance of this method. Numerical results show that the biological networks prefer to use the minimal networks to fulfill their functional tasks, making it possible to apply minimal network criteria in the network reconstruction process. Two scenarios were considered in the reconstruction process: generating data using different initial conditions; and generating data from knock out and over-expression experiments. In both cases, network structures are revealed faithfully in a few steps using our approach. 