Take a look at the Intel Edison, Galileo and Galileo Gen 2 Shields Test Report .You will find a couple of examples for LCD shields, unfortunately yours is not one of them but it will give you an idea on how to start. Have you already tried with this library?
Hi Nepash J
The SEEED Studio Grove RGB LCD is a i2c device that uses smbus for communications, so your connection is correct. The Galileo doesn't access i2c the same way as the Arduino, so I would be very surprised if the Arduino library worked.
If you just want to get the LCD working I posted a message showing how to get it to work with Python
and AlexT's image.
You might be able to get the modified Raspberry Pi library to work with the XDK IoT image, but I haven't tried it.