Recently, nonlinear vector autoregressive (NVAR) model based on Granger causality was proposed to infer nonlinear gene regulatory networks from time series gene expression data. Since NVAR requires a large number of parameters due to the basis expansion, the length of time series microarray data is insufficient for accurate parameter estimation and we need to limit the size of the gene set strongly. To address this limitation, we employ L1 regularization technique to estimate NVAR. Under L1 regularization, direct parents of each gene can be selected efficiently even when the number of parameters exceeds the number of data samples. We can thus estimate larger gene regulatory networks more accurately than those from existing methods. Through the simulation study, we verify the effectiveness of the proposed method by comparing its limitation in the number of genes to that of the existing NVAR. The proposed method is also applied to time series microarray data of Human hela cell cycle.