My friend told me that when using laptop at office or at home, we should use AC current , and cut off battery, or else battery would finished in a short time, Is it true ? How long can a battery last ?

Can somebody help me ? Tks !

What he means is that when your at home or office using the laptop and you don't need to move it from place to place, then keep the ac adapter plugged in, so the battery is always being charged, plug you get maximum runtime, since the laptop is being powered through the ac adaptor.

Also a laptop uses DC current, the plug (AC adaptor) converts AC power to DC which the battery uses. But yes as said above, he means to plug in your laptop so you don't use your battery. A typical battery will last about 3 to 6 hours depending on the type and usage.

Thanks.
One more question : When at home, I use AC (without taking out battery ) and (taking out battery),using which method the battery would have longer life ?

It shouldn't matter. When the laptop detects the ac adapter it will switch to using ac power and charge the battery at the same time. The laptop will know when the battery is fully charged, and will either "trickle-charge" to keep the battery at max. capacity or stop charging, and in essence, "disconnect" the battery.