Network topology represents the influencing mechanism of complex networked system. So it is very important to infer network topology based on the measured data in various fields. In this paper, based on the consideration of nonlinearity, causality and sparsity, a novel method is proposed, termed Block Orthogonal Matching Pursuit-Nonlinear Conditional Granger Causality (BOMP-NCGC). Firstly, Gaussian kernel function is used for fitting the nonlinear system model and the formulation of nonlinear conditional Granger causality is illustrated. Secondly, the block orthogonal matching pursuit is adopted for group sparse selection. Finally, based on the construction of restricted and unrestricted model, nonlinear conditional Granger causality is applied for causal judgement to get the network topology. As a result, the verification of performance is executed by the classical model of gene regulatory network. Compared with linear conditional Granger causality and nonlinear conditional Granger causality, BOMP-NCGC demonstrates the superiority and robustness across the different types of networks.