Greenbrier is a city in Faulkner County, Arkansas, United States. It is part of the Little Rock–North Little Rock–Conway Metropolitan Statistical Area. The population was 5,707 at the 2020 census, up fro…Greenbrier is a city in Faulkner County, Arkansas, United States. It is part of the Little Rock–North Little Rock–Conway Metropolitan Statistical Area. The population was 5,707 at the 2020 census, up from 4,706 at the 2010 census.