Nohup take no effect when to close the terminal end the process running in background?

nohup command means "run command and ignore HUP signals".

So before we can effectively use nohup we need to ask: when and how is SIGHUP sent? As the Bash manual says, "Before exiting, an interactive shell resends the SIGHUP to all jobs, running or stopped.". It goes on to say that the proper way to suppress this behavior is with disown. I realize you are asking about nohup, but it's worth calling out that disown is the intended and easier way to accomplish what you want. Note that disown is not equivalent to nohup.

The reason nohup is tricky to work with here is because it applies to a single process, whereas & creates a background job of a whole command pipeline, which can consist of multiple processes. This means you need to nohup each command in the pipeline in order to ensure that the individual commands don't receive a SIGHUP, e.g.:

$ nohup ls Music/*mp3 2>/dev/null | nohup xargs -d "\n" nohup mplayer &> /dev/null &

This should work, though I haven't tested it with these specific commands. If it doesn't, it's likely another process that you aren't starting directly is still receiving a SIGHUP. This is harder to address, which is exactly why we have disown.

manishg's suggestion is also reasonable; by moving the pipeline into a separate process you can nohup that process, which should in turn prevent a SIGHUP from reaching its children when your shell closes.

All that said, you don't need ls and xargs here in the first place; find can be used to similar effect and will simplify reasoning about the command. Try:

$ nohup find Music -maxdepth 1 -name '*mp3' -exec mplayer {} + &> /dev/null &

I want to play all mp3 music in directory Music.

Usually, you don't need ls or xargs for that.
You can simplify your whole pipeline to mplayer Music/*mp3 ✱.
This is not only safer for special filenames, but also solves your problem with nohup:

nohup mplayer Music/*mp3 &> /dev/null &

nohup doesn’t work like this with pipes. use the following way:

nohup sh -c 'ls  Music/*mp3 |  xargs  -d  "\n"  mplayer' &

There are two way to close the terminal.
exit way:

Input exit in terminal and click enter.

cross way:
Click the cross at the upper right corner.

To illustrate them with same png file. nohup can take effect only with exit way for all the following command(checked everyone at least three times in terminal).

ls Music/*mp3 |xargs -d "\n" nohup mplayer  > /dev/null 2>&1 &
ls  Music/*mp3 | nohup  xargs  -d  "\n"  mplayer  > /dev/null  2>&1  &
nohup ls Music/*mp3 2>/dev/null | nohup xargs -d "\n" nohup mplayer &> /dev/null &
nohup find Music -maxdepth 1 -exec mplayer {} \; &> /dev/null &
nohup mplayer Music/*mp3 &> /dev/null &

A little bug for both nohup sh -c and nohup bash -c:

nohup sh -c 'ls  Music/*mp3 |  xargs  -d  "\n"  mplayer' &
[1] 4581
nohup: ignoring input and appending output to 'nohup.out'
nohup bash -c 'ls  Music/*mp3 |  xargs  -d  "\n"  mplayer' &
[1] 16831
nohup: ignoring input and appending output to 'nohup.out'

When to close terminal with cross way ,music will not play in background for all above command.

The command ending with disown will go on to play the music in background with whatever way (exit or cross way).
It is better to exec disown command in order to go on to play music in background after closing the terminal.