Abstract: By using the function decomposition of the central Morrey spaces with variable exponent and hierarchical estimation methods, and with the help of the boundedness of the parameterized Marcinkiewicz integral operators with rough kernels on the  Lebesgue spaces with variable exponent, we gave the boundedness on the central Morrey spaces with variable exponent.

Key words: parameterized Marcinkiewicz integral, central Morrey spaces with variable exponent, boundedness, rough kernel