A novel numerical algorithm is proposed to reconstruct a complex object from two Gabor in-line holograms. With this algorithm, both the real and imaginary parts of the complex amplitude of the wave front in the object field can be retrieved, and the "twin-image" noise is eliminated at the same time. Therefore, the complex refractive index of the object can be obtained without disturbance. Digital simulations are given to prove the effectiveness of this algorithm. Some practical experimental conditions are investigated by use of error estimation.