A new optical component named linear radial gradient-index lens (LRGIL) for generating Bessel beams with long non-diffracting distance and high beam quality is proposed. Based on the geometrical optics and the diffraction integral theory, the principle of LRGIL generating Bessel beams is analyzed. Using Math CAD to simulate the beam propagation process, LRGIL has the function of traditional axicons and the diffraction-free distance of the Bessel beam is variable with the thickness and the gradient index of LRGIL. A long diffraction-free distance up to 3 m is also obtained in the simulation. Besides, LRGIL has other advantages such as more durable and flexible, it has great potential applications in experiment and production.