In a Sunday speech shown late Wednesday on state television, Castro said that "someone very strange, with very little promise, has taken charge of the leadership of the great empire that we have as a neighbor."
"That gentleman has arrived there, and hopefully he is not as stupid as he seems, nor as mafia-like as his predecessors were," the Cuban leader said. He added, however, that he was not troubled by Mr. Bush's presence, saying "he's there, and we are calm over here."
The United States "cannot invent anything against us," said Castro.
Mr. Bush is the 10th American president to serve since the 1959 triumph of Castro's revolution.
The new U.S. president has expressed support for the four-decade American trade embargo on Cuba. He has said he envisions no change in U.S. policy toward the communist island unless free elections are held and political prisoners are freed.
During last year's presidential campaign, Castro described Mr. Bush, a Republican, and Democratic candidate Al Gore as "boring and insipid."