Direct numerical simulations are performed to investigate the transient growth of a steady disturbance induced by a numerically generated Gaussian rough wall in a laminar boundary layer. In the calculation of the interaction between the rough wall and the fluid, the multiple direct force and immersed boundary method (MDF/IBM) are adopted. The evolution of the streak structures and the energy of the disturbances generated by the rough wall are presented. A similar evolution into an almost sinusoidal modulation for the cylindrical roughness element is found for the current irregular rough wall and the disturbance energy also undergoes the classical transient growth mode. Moreover, the influences of the skewness, kurtosis and correlation length on the evolution of spanwise harmonics are also analyzed. The results show that the effects of skewness and kurtosis are on the distribution of energy among the wavelengths and the subsequent growth processes, while the wavelengths of the harmonics are linked to both the streamwise and spanwise correlation lengths of the rough wall.