Granby was once part of Hadley, as were other towns. Granby was first settled in 1727 and was officially incorporated in 1768. The town is named in honor of John Manners, Marquess of Granby, a hero of the Seven Years’ War. Granby was originally part of the Hadley Equivalent Lands, and then part of South Hadley, before being incorporated on June 11, 1768. Old Hadley was first settled in 1659 by people from Hartford and Wethersfield, Connecticut. These settlers left Connecticut because of religious differences within their communities. John Pynchon was commissioned to buy wilderness land for their new community. Pynchon purchased the land from three Native American chiefs: Chickwallop, Umpanchala and Quontquont. Ownership was transferred to the settlers and confirmed by the General Court. These original boundaries include part of present-day Granby.

Granby is one of only three towns in Massachusetts whose local telephone service is not furnished by the former Bell System as Granby has always maintained its own service, Granby Telephone & Telegraph. The other two such towns are Richmond and Hancock, both in Berkshire County.

According to the United States Census Bureau, the town has a total area of 28.1 square miles (72.7 km²), of which 27.8 square miles (72.1 km²) are land and 0.27 square miles (0.7 km²), or 0.92%, is water. Granby is bordered by South Hadley to the west, Amherst to the north, Belchertown to the east, and Ludlow and Chicopee to the south. Two highways pass through the town: U.S. Route 202 runs eastward though town from South Hadley to Belchertown on East State Street and West State Street, while Route 116 runs northeastward from South Hadley to Amherst along Amherst Road. Granby is 13 miles (21 km) north of Springfield, the largest city in western Massachusetts.

The Holyoke Range is in the northern part of Granby. Major peaks within the town are Long Mountain and Mount Norwottuck. Norwottuck is the highest point in town at 1,106 feet (337 m) above sea level. The Metacomet-Monadnock Trail runs along this mountain range as it passes through Granby. The Horse Caves are geological ledges along this trail.

The public school system in Granby consists of East Meadow and Granby Jr/Sr High School. Grades Pre-K–6 are housed in East Meadow, and grades 7–12 are housed in Granby Jr./Sr. High School.

As of the census of 2000, there were 6,132 people, 2,247 households, and 1,662 families residing in the town. The population density was 220.1 people per square mile (85.0/km²). There were 2,295 housing units at an average density of 82.4 per square mile (31.8/km²). The racial makeup of the town was 96.77% White, 0.51% Black or African American, 0.13% Native American, 0.96% Asian, 0.02% Pacific Islander, 0.52% from other races, and 1.09% from two or more races. Hispanic or Latino of any race were 1.21% of the population.

There were 2,247 households, out of which 34.5% had children under the age of 18 living with them, 62.8% were married couples living together, 8.2% had a female householder with no husband present, and 26.0% were non-families. Of all households, 20.1% were made up of individuals, and 7.9% had someone living alone who was 65 years of age or older. The average household size was 2.71 and the average family size was 3.15.

In the town, the population was spread out, with 25.5% under the age of 18, 7.0% from 18 to 24, 30.6% from 25 to 44, 25.2% from 45 to 64, and 11.7% who were 65 years of age or older. The median age was 38 years. For every 100 females, there were 96.0 males. For every 100 females age 18 and over, there were 94.3 males.

The median income for a household in the town was $54,293, and the median income for a family was $57,632. Males had a median income of $40,833 versus $30,597 for females. The per capita income for the town was $23,209. About 1.0% of families and 2.2% of the population were below the poverty line, including 2.8% of those under age 18 and 2.0% of those age 65 or over.