Is there a way to install Ubuntu on usb pendrive as normal instalation (not live cd)? [duplicate]

Yes.

1.Boot LiveCD from cd,dvd or another pendrive.

2.Insert empty pendrive.

3.Install Ubuntu on empty pendrive.

Based on what @zuberuber says you can even install it on SD Card. With the proper adaptor or natively on sd card embedded laptops. This is how I am writting this: Installed in a 16GB SDCard with 10.5GB Free.

Anyway I suggest you to disconnect all your hard disk drives in your computer, specially those which are having a OS installed (Windows, Linux, etc.) as you may finish having a multi-boot USB/SD Memory with GRUB and in certain cases the bootloader can be written in a different device, other than the USB Memory/SD Card.

Good luck!

Yes, the Startup Disk Creator that comes pre-installed in ubuntu (usb-creator-gtk) allows a persistent option while creating a live-usb install.

Increase the space to whatever you find reasonable. Persistence gives you the freedom to save changes, in the form of settings or files etc, during the live session and the changes are available the next time you boot via the usb drive.

usb-creator limits your live persistent partition size to 4gb, though. To bypass that limit, you would need to edit the partition, and re-size it using a partition editor (such as gparted).

See Live Usb Persistent on the ubuntu wiki for more information.