Morgan is a city in Bosque County in Central Texas, United States.

According to the United States Census Bureau, the city has a total area of 0.8 square miles (2.1 km2), all land.

The climate in this area is characterized by hot, humid summers and generally mild to cool winters.

There were 197 housing units at an average density of 263.8 per square mile (101.9/km2).

23.2% of all households were made up of individuals, and 13.4% had someone living alone who was 65 years of age or older.