Too much current can damage a battery - heating and possible bursting of the battery. How much current a battery will take or draw (however you want to look at it) depends on the voltage applied. Quite often a simple charger will have more than enough DC voltage available to maintain some selected amount of charging current - then the current is controlled or limited.
In better chargers quite a bit of current can be applied while the charger monitors voltage and battery temperature.
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I understood now. Its like if we apply constant voltage source then, the battery would draw large current due to initial low resistance, which may exceed the current rating of the battery. So it always safe to use a constant current source to charge the battery. Am I right?