Circular slab waveguides are conformally mapped into straight waveguides. In the outer cladding region with monotonically increasing index profile, modified Airy functions (MAF) of traveling-wave form are introduced to express the leaky mode. Field distributions and losses calculated by the proposed method are compared with those obtained by the WKB (Wentzel-Kramers-Brillouin) method. Detailed numerical examples are presented and compared with the conventional WKB methods, demonstrating our method not only allows a converging field at turning points but also guarantees fine accuracy.