  In this paper, we discuss the In\"on\"u-Winger contraction of the conformal
algebra. We start with the light-cone form of the Poincar\'e algebra and extend
it to write down the conformal algebra in $d$ dimensions. To contract the
conformal algebra, we choose five dimensions for simplicity and compactify the
third transverse direction in to a circle of radius $R$ following Kaluza-Klein
dimensional reduction method. We identify the inverse radius, $1/R$, as the
contraction parameter. After the contraction, the resulting representation is
found to be the continuous spin representation in four dimensions. Even though
the scaling symmetry survives the contraction, but the special conformal
translation vector changes and behaves like the four-momentum vector. We also
discussed the generalization to $d$ dimensions.
