Reconstruction of networks underlying complex systems is one of the most crucial problems in many areas of engineering and science. In this paper, rather than identifying parameters of complex systems governed by pre-defined models or taking some polynomial and rational functions as a prior information for subsequent model selection, we put forward a general framework for nonlinear causal network reconstruction from time-series with limited observations. With obtaining multi-source datasets based on the data-fusion strategy, we propose a novel method to handle nonlinearity and directionality of complex networked systems, namely group lasso nonlinear conditional granger causality. Specially, our method can exploit different sets of radial basis functions to approximate the nonlinear interactions between each pair of nodes and integrate sparsity into grouped variables selection. The performance characteristic of our approach is firstly assessed with two types of simulated datasets from nonlinear vector autoregressive model and nonlinear dynamic models, and then verified based on the benchmark datasets from DREAM3 Challenge4. Effects of data size and noise intensity are also discussed. All of the results demonstrate that the proposed method performs better in terms of higher area under precision-recall curve.