The problem of the diffraction of a plane wave by the convex surface of a paraboloid of revolution is solved. An infinite set of equations is obtained for the coefficients of the pressure fields inside of and outside of the paraboloid. For the particular case of a rigid paraboloid the coefficients of the series for the scattered field can be obtained explicitly. The ratio of the total pressure at the nose of the paraboloid to the pressure of the incident wave is shown as a function of the shape of the paraboloid for a plane wave whose wave front is perpendicular to the axis of revolution. The same quantity is plotted for the case of a sphere whose radius of curvature is equal to that of the paraboloid at the nose.