A new type of spot-size converter is proposed based on the self-focusing effect of a graded-index waveguide. The field distributions and propagation characteristics of the modes in the uniform-index waveguides and the graded-index waveguides are investigated. In addition, the principle of self-focusing effect is analyzed. With the finite-difference time-domain method, the insertion loss and the return loss of the proposed converter are calculated. The performance of the proposed converter is as good as that of the existing best device, however the length of the proposed converter is reduced to 1/6 of the the existing best device. The novel spot-size converter can be used in the integrated optics.