A charging control method, for use in controlling a charging circuit to provide a charging power to a battery , wherein the charging power includes a charging voltage (VBAT) and a charging current (IBAT), and the charging circuit includes a power delivery unit and one or more capacitive power conversion circuits , wherein the power delivery unit converts an input power to a DC output power, the DC output power including a DC output voltage (VBUS) and a DC output current (IDC); and wherein the capacitive power conversion circuit comprises a conversion switch circuit which includes plural conversion switches (SW11, SW12, SW13, SW14), and one or more conversion capacitors (CA1-CAN) coupled to the conversion switch circuit ; characterized in that the charging control method comprises: during a constant-current charging stage, regulating the DC output current (IDC) to a predetermined constant output current level by the power delivery unit ; and during the constant-current charging stage, converting the DC output current (IDC) to the charging current (IBAT) by the capacitive power conversion circuit such that the level of the charging current (IBAT) is constant and is scaled-up of the predetermined constant output current level by a predetermined factor so that the battery is charged with constant-current, the factor being larger than 1 whereby the charging current (IBAT) is larger than the DC output current (IDC), wherein a voltage of the battery varies with time when the battery is charged with constant-current in the constant-current charging stage, and the DC output voltage (VBUS) varies with the voltage of the battery ; wherein the step of converting the DC output power to the charging power includes: during plural conversion time periods, operating the plural conversion switches (SW11, SW12, SW13, SW14) so as to electrically connect the one or more conversion capacitors (CA1-CAN) between a pair of nodes selected from one or more voltage division nodes (ND1-NDM), the DC output voltage (VBUS), and a ground node periodically, wherein the charging power is electrically connected to one of the one or more voltage division nodes (ND1-NDM). during a constant-current charging stage, regulating the DC output current (IDC) to a predetermined constant output current level by the power delivery unit ; and during the constant-current charging stage, converting the DC output current (IDC) to the charging current (IBAT) by the capacitive power conversion circuit such that the level of the charging current (IBAT) is constant and is scaled-up of the predetermined constant output current level by a predetermined factor so that the battery is charged with constant-current, the factor being larger than 1 whereby the charging current (IBAT) is larger than the DC output current (IDC), wherein a voltage of the battery varies with time when the battery is charged with constant-current in the constant-current charging stage, and the DC output voltage (VBUS) varies with the voltage of the battery ; wherein the step of converting the DC output power to the charging power includes: during plural conversion time periods, operating the plural conversion switches (SW11, SW12, SW13, SW14) so as to electrically connect the one or more conversion capacitors (CA1-CAN) between a pair of nodes selected from one or more voltage division nodes (ND1-NDM), the DC output voltage (VBUS), and a ground node periodically, wherein the charging power is electrically connected to one of the one or more voltage division nodes (ND1-NDM). <EOS>