The purpose of this paper is to define the continuous Jacobi transform as an extension of the discrete Jacobi transform. The basic properties including the inversion theorem for the continuous Jacobi transform are studied. We also derive an inversion formula for the transform which maps L 1 ( R + ) into L w 2 ( − 1 , 1 ) where w ( x ) = ( 1 − x ) α ( 1 + x ) β .