The relativistic mean field theory consistent with bulk properties of nuclear matter is extended to study the excitations of the sound-like collective modes in nuclear matter. Corresponding relativistic mean field equations are solved numerically and self-consis-tently. The effective mass of nucleon the speed of the sound and the amplitude of the sound-like solution are calculated. When the nuclear density is near or greater than the saturation density, the sound-like non-trivial solution could be found.