A microphone array system includes a plurality of microphones and a sound signal processing part. The microphones are arranged in such a manner that at least three microphones are arranged in a first direction to form a microphone row, at least three rows of the microphones are arranged so that the microphone rows are not crossed each other so as to form a plane, and at least three layers of the planes are arranged three-dimensionally so that the planes are not crossed each other, so that the boundary conditions for the sound estimation at each plane of the planes constituting the three dimension can be obtained. The sound signal processing part estimates a sound in each direction of the three-dimensional space by estimating sound signals in at least three positions along a direction that crosses the first direction, utilizing the relationship between the gradient on the time axis of the sound pressure and the gradient on the spatial axis of the air particle velocity, and the relationship between the gradient on the spatial axis of the sound pressure and the gradient on the time axis of the air particle velocity, and based on a temporal variation of the sound pressure of the received sound signals of the arranged microphones in each spatial axis direction and a spatial variation of the received sound signals of the arranged microphones.