Cold atmospheric plasma (CAP) jet has wide applications in various fields including advanced materials synthesis and modifications, biomedicine, environmental protection and energy saving, etc. Appropriate control on the volume, temperature and chemically reactive species concentrations of the CAP jet is of great importance in actual applications. In this paper, an radio-frequency atmospheric-pressure glow discharge (RF-APGD) plasma generator with a hybrid cross-linear-field electrode configuration is proposed. The experimental results show that, with the aid of the copper mesh located at the downstream of the traditional co-axial-type plasma generator with a cross-field electrode configuration, a linear field between the inner powered electrode of the traditional plasma generator and the copper mesh can be established. This linerfield can, to some extent, enhance the discharges at the upstream of the copper mesh, resulting in small increments (all less than 12.5%) of the species emission intensities, electron excitation temperatures and gas temperatures by keeping other parameters being unchanged. And due to the intrinsic transparent and conducting features of the grounded copper mesh to the gas flowing, electric current and heat flux of the plasma plumes, a plasma region with higher concentrations of chemically reactive species and larger plasma plume diameters is obtained at the downstream of the grounded copper mesh on the same level of the gas temperature and electron excitation temperature compared to those of the plasma free jet. In addition, the charged particle number densities at the same downstream axial location of the grounded copper mesh decrease significantly compared to those of the plasma free jet. This means that the copper mesh is also, to some extent, helpful for separating the chemically reactive neutral species from the charged particles inside a plasma environment. The preceding results indicate that the cross-linear-field electrode configuration of the plasma generator is an effective approach for tuning the characteristics of the RF-APGD plasma jet in order to obtain an appropriate combination of the plasma jet properties with higher chemically reactive species concentrations, especially relative higher number densities of neutral species, larger plasma volumes and lower gas temperatures.