I have a basic question, that is it possible to assign RS260GS a dynamic IP address by DHCP? If so, how can I do that? I have been confusing about this problem for two days. Help!

I guess you mean the RB260GS.
It is possible since SwitchOS 2.5. Then you can find it under System > General > Address Acquisition. Three options:
* DHCP with fallback
* static
* DHCP only

Thank you Marting! I did the same this morning. But here I have new problems:
(1) Do I need to set proxy server? Because it couldn't be connected to Internet after I updated it to V2.7, and windows shows that it couldn't detect the proxy settings.
(2) When I set the address option to DHCP only mode, how could I connect it from my PC? I use winbox 3.11 but couldn't find it from the neighbour, neither could I connect it via MAC address.

Thank you in advance!

First of all you are mixing different things up. RB260GS is not operated by RouterOS but by SwitchOS (not dualload capable as far as I know). SwitchOS can not be managed with winbox but only with the browser.

The switch does not need internet access at all because he has nothing that relies on internet access. It is a switch, nothing more. The only thing you will need some kind of internet access is for a SwOS upgrade. But internet access is not used as usual, I guess the PC connecting to the switch is somehow used as somthing like a proxy. This is kind of strange for me and it doesn´t work well all the time, but you always can use the manual upload field.

From: https://wiki.mikrotik.com/wiki/SwOS/RB2 ... System_Tab
Note: SwOS uses a simple algorithm to ensure TCP/IP communication - it just replies to the same IP and MAC address packet came from. This way there is no need for Default Gateway on the device itself.

If you don´t have internet access on your Windows PC you probably missconfigured something. If you do not know where to start, then reset the Switch to factory defaults (and SwOS 2.0). Afterwards you have to upgrade to v2.7 and DHCP again. But at this stage (if you did not configure anything else) it is still a dump switch. No port isolation, no vlans, nothing. Each port can talk to each port like with an unmanaged switch. Has nothing to do with a proxy server.

Thanks! I tried to reset the switch and updated it again to V2.7, but it doesn't work as well. The phenomenon is that, when I connect an Internet cable and my PC via this switch, the PC couldn't get access to the Internet, however, it could work when I did the same to another type of switch. Besides, when I select the switch address as "DHCP only" mode, how could I get its dynamic IP?

By looking into the lease table of the router that runs the DHCP server. If you are not able to do so why do you want to use DHCP?
Let's start from beginning. Which router, which subnets, any vlans? Your private lan at home? What if you use static IP for your PC? Does your PC get a DHCP lease?