A charging method on constant current mode, said charging method comprises steps of communicating with a rechargeable battery by a central control module to obtain a first current (I req) and a first voltage (V req) required to charge said rechargeable battery; transmitting a first current output instruction regarding said first current (I req) and a first voltage output instruction regarding said first voltage (V req) by said central control module to a first charging module and a second charging module; receiving said first current output instruction and said first voltage output instruction by said first charging module and said second charging module; outputting a second voltage (V o1) and a second current (I ο1) to said rechargeable battery and transmitting an output value of said second voltage (V o1) and an output value of said second current (I o1) to said central control module by said first charging module, and outputting a third voltage (V o2) and a third current (I o2) to said rechargeable battery and transmitting an output value of said third voltage (V o2) and an output value of said third current (I o2) to said central control module by said second charging module; and characterized in that when said central control module repeatedly and separately detects that difference between said first voltage (V req) and said output value of said second voltage (V o1) is smaller than a predetermined voltage value, transmitting a fourth current output instruction, in which a fourth current (I req_new) equals said first current (I req) minus a predetermined current value, to said first charging module by said central control module, wherein said central control module reduces said first current (I req) with a fixed proportion to form said fourth current (I req_new); when said central control module repeatedly and separately detects that difference between said first voltage (V req) and said output value of said third voltage (V o2) is smaller than said predetermined voltage value, repeatedly transmitting said fourth current output instruction, in which said fourth current (I req_new) equals said first current (I req) minus said predetermined current value, to said second charging module by said central control module. communicating with a rechargeable battery by a central control module to obtain a first current (I req) and a first voltage (V req) required to charge said rechargeable battery; transmitting a first current output instruction regarding said first current (I req) and a first voltage output instruction regarding said first voltage (V req) by said central control module to a first charging module and a second charging module; receiving said first current output instruction and said first voltage output instruction by said first charging module and said second charging module; outputting a second voltage (V o1) and a second current (I ο1) to said rechargeable battery and transmitting an output value of said second voltage (V o1) and an output value of said second current (I o1) to said central control module by said first charging module, and outputting a third voltage (V o2) and a third current (I o2) to said rechargeable battery and transmitting an output value of said third voltage (V o2) and an output value of said third current (I o2) to said central control module by said second charging module; and characterized in that when said central control module repeatedly and separately detects that difference between said first voltage (V req) and said output value of said second voltage (V o1) is smaller than a predetermined voltage value, transmitting a fourth current output instruction, in which a fourth current (I req_new) equals said first current (I req) minus a predetermined current value, to said first charging module by said central control module, wherein said central control module reduces said first current (I req) with a fixed proportion to form said fourth current (I req_new); when said central control module repeatedly and separately detects that difference between said first voltage (V req) and said output value of said third voltage (V o2) is smaller than said predetermined voltage value, repeatedly transmitting said fourth current output instruction, in which said fourth current (I req_new) equals said first current (I req) minus said predetermined current value, to said second charging module by said central control module.