The conical phase shift induced by the axicon generates a non-diffracting Bessel beam. In this paper, we examine the propagation property of an electromagnetic wave focused by a thin lens and axicon waveplate combination, which induces a small amount of conical phase shift less than one wavelength. A general expression describing the focused field distribution has been derived under the paraxial approximation. The conical phase shift breaks the axial symmetry of intensity and shows a focal spot-shaping capability by controlling the central intensity profile within a certain range near focus. The focal spot-shaping capability can be applied to form a concave or flattened intensity profile, which can be used to control the concavity of a double-sided relativistic flying mirror or to generate the spatially uniform and energetic laser-driven proton/ion beams for hadron therapy.