A semi-implicit finite difference scheme with time splitting corresponding to multi-scale nature of the atmospheric dynamics is developed for the nonhydrostatic atmospheric model. The fast acoustic and gravity waves are approximated implicitly, while relatively slow advective terms and Rossby modes are treated explicitly. Applied level of implicity requires solution of three-dimensional linear elliptic equation at each time step, which is accomplished efficiently by employing available multigrid software. Analysis of the linear stability of the scheme reveals that the CFL restriction on time step with respect to both gravity and acoustic waves can be overcome and time step can be chosen in accordance with physical considerations of accuracy. The performed numerical experiments show computational efficiency of the designed scheme and accuracy of the predicted atmospheric fields.