A cellular signal transduction network is an important means to describe biological responses to environmental stimuli and exchange of biological signals. Constructing the cellular signal transduction network provides an important basis for the study of the biological activities, the mechanism of the diseases, drug targets and so on. The statistical approaches to network inference are popular in literature. Granger test has been used as an effective method for causality inference. Compared with bivariate granger tests, multivariate granger tests reduce the indirect causality and were used widely for the construction of cellular signal transduction networks. A multivariate Granger test requires that the number of time points in the time-series data is more than the number of nodes involved in the network. However, there are many real datasets with a few time points which are much less than the number of nodes in the network. In this study, we propose a new multivariate Granger test-based framework to construct cellular signal transduction network, called MGT-SM. Our MGT-SM uses SVD to compute the coefficient matrix from gene expression data and adopts Monte Carlo simulation to estimate the significance of directed edges in the constructed networks. We apply the proposed MGT-SM to Yeast Synthetic Network and MDA-MB-468, and evaluate its performance in terms of the recall and the AUC. The results show that MGT-SM achieves better results, compared with other popular methods (CGC2SPR, PGC, and DBN).