A constant-current battery charger includes a power supply for supplying a charge current to a secondary cell, and a current monitor for monitoring a charge current being supplied to the cell. A controller is included for varying the charge current in accordance with the monitored charge current. The controller calculates a current difference between a predetermined target current and the instant charge current, and generates a demand of varying the charge current at a first charge rate when the current difference is out of a predetermined range, and varying the charge current at a second charge rate when the current difference is within the predetermined range. The controller generates the demand repeatedly at regular or varying intervals for varying the charge current. The first charge rate is set to be higher than the second charge rate in order to make a rapid charging until it comes close to the target current. Since the current difference between the instant charge current and the target current is relied upon to switch the charge rate between the first and second charge rates, the switching can be made at an exact timing truly indicative of the condition of the battery, which enables a rapid charging, yet assuring to complete the charging successfully.