Imjpmig.exe process belongs to the Microsoft Input Method Editor. It is a legitimate system process, so it shouldn't be stopped or removed. It's main uses is to simplify the input for asian characters in Microsoft Office suite (Japanese keyboard entry). Imjpmig.exe is located in “C:\windows\IME\imjp8_1\” on Windows XP.
Some modern parasites might use imjpmig.exe process name for hiding their real name, however, it's less likely to happen. If it happened for you, check your system with SpyHunter 5 – it will make sure your computer is safe from viruses and parasites. However, if you don't check your PC with a legitimate anti-spyware tool, don't kill this process! it's essential for proper functioning of Windows.