A new member of the 2D carbon family, grapheneplus (G+), has demonstrated excellent properties, such as Dirac cones and high surface area. In this study, the electronic transport properties of G+, NG+, and BG+ monolayers in which the NG+/BG+ can be obtained by replacing the center sp3 hybrid carbon atoms of the G+ with N/B atoms, were studied and compared using density functional theory and the non-equilibrium Green's function method. The results revealed that G+ is a semi-metal with two Dirac cones, which becomes metallic upon doping with N or B atoms. Based on the electronic structures, the conductivities of the 2D G+, NG+ and BG+-based nanodevices were analyzed deeply. It was found that the currents of all the designed devices increased with increasing the applied bias voltage, showing obvious quasi-linear current-voltage characteristics. IG+ was significantly higher than ING+ and IBG+ at the same bias voltage, and IG+ was almost twice IBG+, indicating that the electron mobility of G+ can be controlled by B/N doping. Additionally, the gas sensitivities of G+, NG+, and BG+-based gas sensors in detecting C2H4, CH2O, CH4O, and CH4 organic gases were studied. All the considered sensors can chemically adsorb C2H4 and CH2O, but there were only weak van der Waals interactions with CH4O and CH4. For chemical adsorption, the gas sensitivities of these sensors were considerably high and steady, and the sensitivity of NG+ to adsorb C2H4 and CH2O was greater as compared to G+ and BG+ at higher bias voltages. Interestingly, the maximum sensitivity difference for BG+ toward C2H4 and CH2O was 17%, which is better as compared to G+ and NG+. The high sensitivity and different response signals of these sensors were analyzed by transmission spectra and scattering state separation at the Fermi level. Gas sensors based on G+ monolayers can effectively detect organic gases such as C2H4 and CH2O, triggering their broad potential application prospects in the field of gas sensing.