No-insulation (NI) Rare-Earth Barium Copper Oxide (REBCO) pancake coils can generate high magnetic fields and have the high thermal stability against normal-state transition due to allowing currents to radially bypass a local normal-state region through the turn-to-turn contacts. Despite these merits, no turn-toturn insulation causes a charging delay. To solve this charging delay problem, an NI REBCO coil wound with multi-bundled (MB) conductors was proposed. As an experimental result, a charging delay was improved because the inductance per tape of MB coil is smaller than that of single-tape NI coil. Meanwhile, the current behaviors of MB coils are complicated and has not been clarified. We have investigated the current and thermal behaviors of MB REB-CO coils during charging and against normal-state transition, comparing with and without turn-to-turn insulation. As the result, it is shown that the MB coil can be operated stably, and no pessimistic temperature rise is observed. However, the operating current of MB coils with turn-to-turn insulation may concentrate on one tape when the normal-state transition occurs. Therefore, MB coils without turn-to-turn insulation seems to be desirable. Index Terms-Charging delay, high magnetic field generation, multi-bundled REBCO tape, no-insulation winding technique.