I want to know if there is a word that has similar meaning to "community", "society", "country" or any word describes a group of people. but the special thing in this group or this place is that there are people from different nations or different communities happened to be in that same place. Is there a word like that?
Such a place is said to be cosmopolitan. Here are examples from the Oxford Learner's Dictionaries:
A cosmopolitan city/resort
Jamaica is a very cosmopolitan island
Below I've collected some phrases I was able to find in various documents as well as ones that I thought of. I've roughly sorted them from phrases I could imagine being used in common speech to those found in government or clinical contexts.
Generally the words "global" or "international" will put emphasis on people who have traveled from another part of the world, or still have strong connections to other regions while "diverse" focuses more on the cultural differences and does not address the people's origins.
I've a friend from a village in India called Auroville. He would refer to it as in international village, thought the government seems to prefer to call it a universal city. http://www.auroville.org/
I think most people would understand global city to mean a city with many international connections, but I think it comes from a well defined ranking based on financial connections. Wiki: Global City
This term is discussed in American studies to refer to the idea that people would assimilate into culture—melt into uniformity. Depending on region this may be true to an extent, but I feel that there is always a merging of culture. This phrase must be used carefully because of the extensive background of its usage. Wiki: Melting Pot
In American English diverse usually means "not white", and is often used in media to discuss demographics. I've linked to a Forbes post about which cities in America have the most diverse population. I'm from San Jose and I can attest that residents of San Jose generally consider there to be three major racial groups: White, Mexican, and Asian. Forbes: Diversity in America
Diverse populations is a term that comes up in technical and social work contexts to discuss groups of people. Office of Adolescent Health training material, Psychologists: Reaching Out to Diverse Populations: Opportunities and Challenges
Although it does not directly mean 'a group or society' perhaps multicultural would suit your needs. "The community was multicultural","This is a multicultural society".