This paper presents simulations of the dynamics of surface charging by an air plasma discharge at atmospheric pressure initiated by a needle anode inside a capillary glass tube. During the discharge propagation in the tube, the highest positive surface charge density is observed close to the point electrode. We have shown that during the discharge propagation, the positive surface charge is increasing behind the discharge front, while the electric field at the surface is decreasing. Then, we have studied the influence of the tube radius, its permittivity and the applied pulsed voltage on surface charges. We have shown that the surface charge density during the discharge propagation is inversely proportional to the tube radius and surface charge densities of 30–50 nC/cm2 for a tube with Rtube = 100 μm and an applied voltage of 12 kV have been obtained. We have also noted that a higher permittivity results in a higher surface charge density and a faster surface charge deposition. Then we have shown that the surface charge deposited is proportional to the applied voltage. Finally, at the end of the voltage pulse, our simulations indicate that the positive surface charge deposited during the discharge propagation in the tube decreases to very low values in few nanoseconds.