Yes, certain dependents can travel to the United States with you and live with you in America if you have a valid H-1 visa. However, they must first apply for an H-4 visa for dependents to obtain their own visa.
Your spouse and unmarried children under the age of 21 may apply for an H-4 visa for dependents. With this visa, they will be able to attend school full-time, but they will not be able to seek employment or work in the United States. The H-4 visa allows your family to travel freely throughout the country and the world, and is valid for as long as the H-1 visa holder’s paperwork is current. An H-4 visa can be extended just as an H-1 visa can be extended.
If you would like to work while in the United States on an H-4 visa, you must change your visa status. Likewise, if you are a child of an H visa holder and turn 21 while studying in the United States, you must change your visa status in order to legally continue your education.