An improved gaseous fuel burner system for minimizing the production of NOx in a gas burner, comprising a primary burner, including a burner tube and a primary burner head, having a plurality of primary burner ports, in a two dimensional array, over a selected, substantially planar area, transverse to the burner tube. A mixture of gaseous fuel and primary air is supplied to the burner tube, and to the primary burner ports. Secondary combustion air is supplied around the burner tube and flows downstreamwardly to the primary burner and to the combustion zone downstream of the primary burner ports. Secondary burner ports are provided upstream of the primary burner ports, which carry the gaseous fuel and primary air in the form of jets, mixing with the secondary air, and burning to provide combustion products CO.sub.2 and H.sub.2 O, which flow downstreamwardly with the secondary air into the combustion zone of the primary burner.