In clinical practice, brain SPECT is mostly performed using a dual-head SPECT scanner with fan-beam or parallel-beam collimators rotating around the patient's head. The resolution of such a system is typically about 6-8 mm, which is rather poor to image the complex structures of the human brain. We developed a non-rotating multi-pinhole collimator for brain SPECT imaging with a resolution of 4 mm. A full-ring geometry allows for complete transaxial sampling. This enables the use of a stationary collimator. The collimator is a tungsten ring with two rows of pinholes. Each pinhole can individually be opened or closed with shutters. A sequence of shutter movements is performed to obtain an acquisition setup that simulates a rotational movement. The collimator is designed for the LaPET system (a PET detector ring made of 24 LaBr3 detectors) and is optimized to maximize the system performance, resulting in a collimator radius of 145 mm and a pinhole diameter of 2 mm. This system has a sensitivity that is 4 times lower than a dual-head system with LEHR parallel-beam collimators. However, the resolution is 2 times better, a trade-off that is supported by Muehllehner [1]. Monte-Carlo simulated projections of a resolution phantom are successfully reconstructed and the resulting image shows that a resolution of 4 mm is indeed achieved.