The potential of Multiple Pinhole Arrays (MPA) collimators for developing a Single Photon Emission Computer Tomography (SPECT) system without rotating or moving elements is investigated. A four layer arrangement is proposed and the system performance is evaluated using the simulation toolkit GATE [1]. For a camera with a field of view (FOV) of the order of a human brain (a sphere of radius 100 mm), a sensitivity of 86, 0 cps/MBq and an overall resolution of 5 mm have been estimated, indicating that performances comparable to traditional parallel-hole-collimator cameras can be achieved.