As of the census of 2000, there were 395 people, 156 households, and 114 families residing in the city. The population density was 3,362.7 people per square mile (1,270.9/km²). There were 165 housing units at an average density of 1,404.7 per square mile (530.9/km²). The racial makeup of the city was 96.46% White, 1.01% African American, 0.76% Asian, 0.25% from other races, and 1.52% from two or more races. Hispanic or Latino of any race were 0.76% of the population.

There were 156 households out of which 33.3% had children under the age of 18 living with them, 62.8% were married couples living together, 7.1% had a female householder with no husband present, and 26.9% were non-families. 22.4% of all households were made up of individuals and 7.1% had someone living alone who was 65 years of age or older. The average household size was 2.53 and the average family size was 2.97.

In the city of Norwood KY the population was spread out with 27.1% under the age of 18, 4.8% from 18 to 24, 26.6% from 25 to 44, 27.3% from 45 to 64, and 14.2% who were 65 years of age or older. The median age was 40 years. For every 100 females there were 107.9 males. For every 100 females age 18 and over, there were 94.6 males.

The median income for a household in the city was $65,833, and the median income for a family was $71,250. Males had a median income of $61,406 versus $31,923 for females. The per capita income for the city was $29,092. About 5.5% of families and 4.4% of the population were below the poverty line, including 4.8% of those under age 18 and 14.7% of those age 65 or over.