In answering this question, I will assume that you are asking about the Red Scare that occurred after World War I. There are at least three main reasons for this scare.
The first reason for the Red Scare was the fact that the Soviet Union had just become a communist country. This was the first country in the world to become communist. The idea that communists in one country could overthrow the country’s government made many Americans fear that it was possible that the same thing would happen in the United States.
The second reason for the Red Scare was immigration. In the decades before World War I, there had been tremendous amounts of immigration to the US. Many of the immigrants held rather radical political beliefs. Therefore, many Americans were worried that the immigrants would support communists who might want to overthrow the US government.
Finally, there was the fact that there was a great deal of labor unrest after WWI. There were, for example, a police strike in Boston and a general strike in Seattle in 1919. These sorts of strikes seemed to many to be inspired by communists. When these strikes arose, many Americans feared that a communist rebellion was already brewing.
For these reasons, the Red Scare occurred after WWI.