Plasmonic waveguides and conventional dielectric waveguides have favorable characteristics in photonic integrated circuits. Typically, plasmonic waveguides can provide subwavelength mode confinement, as shown by their small mode area, whereas conventional dielectric waveguides guide light with low loss, as shown by their long propagation length. However, the simultaneous achievement of subwavelength mode confinement and low-loss propagation remains limited. In this paper, we propose a novel design of an alldielectric bowtie waveguide, which simultaneously exhibits both subwavelength mode confinement and theoretically lossless propagation. Contrary to traditional dielectric waveguides, where the guidance of light is based on total internal reflection, the principle of the all-dielectric bowtie waveguide is based on the combined use of the conservation of the normal component of the electric displacement and the tangential component of the electric field, such that it can achieve a mode area comparable to its plasmonic counterparts. The mode distribution in the all-dielectric bowtie waveguide can be precisely controlled by manipulating the geometric design. Our work shows that it is possible to achieve extreme light confinement by using dielectric instead of lossy metals.