Reconstruction of genetic networks is one of the key scientific challenges in functional genomics. This paper describes a novel approach for addressing the regulatory dependencies between genes whose activities can be delayed by multiple units of time. The aim of the proposed approach termed TdGRN (time-delayed gene regulatory networking) is to reversely engineer the dynamic mechanisms of gene regulations, which is realized by identifying the time-delayed gene regulations through supervised decision-tree analysis of the newly designed time-delayed gene expression matrix, derived from the original time-series microarray data. A permutation technique is used to determine the statistical classification threshold of a tree, from which a gene regulatory rule(s) is extracted. The proposed TdGRN is a model-free approach that attempts to learn the underlying regulatory rules without relying on any model assumptions. Compared with model-based approaches, it has several significant advantages: it requires neither any arbitrary threshold for discretization of gene transcriptional values nor the definition of the number of regulators (k). We have applied this novel method to the publicly available data for budding yeast cell cycling. The numerical results demonstrate that most of the identified time-delayed gene regulations have current biological knowledge supports.