Regulation of gene expression is fundamental to the operation of a cell. Revealing the structure and dynamics of a gene regulatory network (GRN) is of great interest and represents a considerably challenging computational problem. The GRN estimation problem is complicated by the fact that the number of gene expression measurements is typically extremely small when compared with the dimension of the biological system. Further, because the gene regulation process is intrinsically complex, commonly used parametric models can provide too simple description of the underlying phenomena and, thus, can be unreliable. In this article, we propose a novel methodology for the inference of GRNs from time-series and steady-state gene expression measurements. The presented framework is based on the use of Bayesian analysis with ordinary differential equations (ODEs) and non-parametric Gaussian process modeling for the transcriptional-level regulation.