Recent progresses in the protein regulatory network of budding yeast Saccharomyces cerevisiae have provided a global picture of its protein network for further dynamical research. We simplify and modularize the protein regulatory networks in yeast nucleus, and study the dynamical properties of the core 37-node network by a Boolean network model, especially the evolution steps and final fixed points. Our simulation results show that the number of fixed points N(k) for a given size of the attraction basin k obeys a power-law distribution N(k)∝k-2.024. The yeast network is more similar to a scale-free network than a random network in the above dynamical properties.