High temperature superconductor (HTS) no-electrical-insulation (NEI) coils demonstrate great advantages in thermal stability and self-protection features. However, an intrinsic delay is observed in the charging process and as a result there maybe a possible settle-out problem. It becomes more critical for large HTS coils with more turns, such as the magnets for the accelerator system and DC induction heater applications. This paper presents detailed studies on the charging characteristics of NEI coils. Firstly, two different no-electrical-insulation coils are wound: the first is directly wound using only REBCO tapes with brass lamination, which is called a no-insulation (NI) coil. The other one is co-wound with stainless steel (SS) strips and REBCO tapes whose copper stabilizer is electroplated, which is called a metallic insulation (MI) coil. Fast discharging tests are performed on the two coils and their equivalent turn-to-turn resistivity is calculated. A similar discharging delay is observed on both coils, but the turn-to-turn resistivity of the SS co-wound coil is much higher than that of the first coil. Then the resistivity data is directly applied to an equivalent circuit network model which is developed to predict the charging behaviours. The model calculates coil voltage, currents along the azimuthal and radial directions, as well as the induced magnetic field. A practical charging time is defined to characterize the field ramping process considering the charging delay between field ramping and current charging. The charging behaviours are extensively analyzed and compared in terms of three primary factors: equivalent turn-to-turn resistivity, coil size and ramping rate. The results show that the charging time increases dramatically with the coil size and may be too long to be practical for large-scale applications using HTS coils with low turn-to-turn resistivity. Increasing the turn-to-turn resistivity enables one to accelerate the charging process effectively. Therefore, the SS co-wound coil with higher turn-to-turn resistivity shows a much shorter charging time, which indicates that it may be more suitable for large-scale HTS magnets.