When tomography is performed with strongly refracting field, refraction may cause sufficient bending of the probing rays. Ordinary reconstruction algorithm, based on the assumption of straight rays, does not yield accurate results. A new approach to curved-ray tomographic reconstruction of strongly refracting refractive-index distribution is proposed to realize a nonlinear inversion. A digital ray tracing method is designed for calculation of ray trajectory in inhomogeneous media. An initial estimate of the field is made by algebraic reconstruction technique. This estimate is then corrected by an iterative process in which computational ray tracing is used to generate deflection angles that are indirectly compared with the measured values. The reconstruction technique was tested by using simulated projection data of strongly refracting field for incomplete projection situation, and some reconstructed errors were discussed.