Two major challenges in inferring the sparse topological architecture of Gene Regulatory Networks using computational methods are 1) the low accuracy of predicting connections between genes and 2) the excessive computational cost. In order to address these challenges, we have exploited some biological features of yeast cell cycle. One such feature is that, a high proportion of Cell Cycle Regulated genes are periodically expressed; that is genes are maximally expressed to affect and control the regulation of other genes and on completing certain tasks; they are repressed by some other regulator genes. Thus the whole cell cycle progresses systematically through the successive activation and inactivation of CCR genes. To use this feature, we have calculated the peak time of individual genes which falls into one/more phases of the cell cycle. Therefore, genes that peak in the interval of the same phase of the cell cycle have been grouped together. Finally, we have applied the Dynamic Bayesian Network (DBN) algorithm within distinct phases of genes. As a consequence, both the accuracy and the computational cost of our learning algorithm have been improved in comparison with the existing DBN algorithms.