We present an integral equation method for conformal mapping of doubly connected regions onto a unit disc with circular slit of radius m < 1. Our theoretical development is based on the boundary integral equation for conformal mapping of doubly connected region derived by Murid and Razali. In this paper, using the boundary relationship satisfied by the mapping function, a related system of Fredholm integral equation is constructed, provided m is assume known. For numerical experiment, the integral equation is discretized which leads to a system of linear equations. Numerical implementation on a circular annulus is also presented
