This study investigates how addition of a 2nd ground electrode in an argon plasma jet influences the production of hydrogen peroxide (H2O2) in deionised water (DIW). Briefly, plasma is ignited by purging argon gas through a quartz tube at 1 l min-1 and applying a sinusoidal voltage of 7 kV (peak-peak) at 23.5 kHz to a high voltage stainless steel needle electrode sealed inside the quartz tube surrounded by one or two copper ring(s) that served as the ground electrode(s) situated downstream of the high voltage electrode. The mechanisms of H2O2 production are investigated through the electrical and optical plasma properties and chemical analysis of the treated DIW. We discover that the addition of a 2nd ground electrode results in higher accumulation of charges on the inner wall surface of the quartz tube of the plasma jet assembly resulting in an increase in the discharge current and dissipated power. This further leads to an increase in the electron temperature that more than doubles the H2O2 production through dissociative recombination of water vapour molecules, whilst still maintaining a biological tissue tolerable gas temperature. The double ground electrode plasma jet is shown to be highly effective at reducing the growth of common wound pathogens (Pseudomonas aeruginosa and Staphylococcus aureus) in both planktonic and biofilm states whilst inducing a low level of cytotoxicity in HaCaT keratinocyte skin-like cells under certain conditions. The information provided in this study is useful in understanding the complex physicochemical processes that influence H2O2 production in plasma jets, which is needed to optimise the development of plasma sources for clinical applications.