I want to use accelerometer of iPhone to get the log file of accelerometer value (maybe for 24 hours). Is it possible to let accelerometer runs in background while other applica
Nope, it is not. You basically can't run anything but a music app in the background.
You can run the accelerometer while the phone is suspended though.
See this blog for how to do it: http://marcopeluso.com/2009/08/23/how-to-prevent-iphone-from-deep-sleeping/
I use this technique in my GPS recording app.