A novel numerical algorithm is proposed to reconstruct the Laplacian of an object field from one single in-line hologram. This method uses two different reconstruction distances of z and z+\Delta z, or two different reconstruction wavelengths of \lambda and \lambda + \Delta to reconstruct one digital in-line hologram. Theoretical analysis shows that when the value of \Delta z or \Delta \lambda is sufficiently small, the difference of the two reconstructed fields is an approximation to the second-order Laplacian differentiation of the object wave, and the zero-order and "twin-image" noise can be almost eliminated simultaneously. Computer numerical simulations and optical experiments are carried out to validate the effectiveness of this algorithm.