This article analyzes the charging behavior of no-insulation high temperature superconducting (HTS) ReBCO double-cake coils under conduction cooling and liquid nitrogen cooling in detail. A partial equivalent circuit model of a determined parameter ReBCO coil is applied to evaluate charging behavior under different cooling conditions. At the same time, the finite element method is used to couple the circuit model with the magnetic field model and the heat transfer model to analyze the changes of the current distribution, magnetic field and temperature of the coil during the charging process. The simulation results obtained by numerical calculation using the coupled model are in good agreement with the results of coil charging experiments under conduction cooling conditions, which also verifies the correctness of the proposed coupled model. In addition, numerical simulation and experiment of different charging rates were carried out under conduction cooling conditions to analyze the excitation characteristics of no-insulation high temperature superconducting magnets in detail.