Abstract-A new design of collimator is proposed that has variable sensitivity and spatial resolution, eliminating the need for exchanging collimators in a gamma camera. Using Monte Carlo simulations, the present article evaluates the shielding of undesirable gamma rays in a parallel-hole collimator. It consists of a number of layers of rectangular holes. These layers consist of alternately stacked fixed and movable collimators. In high-resolution mode, the movable collimators are shifted by half the aperture pitch along the diagonal direction. The first collimator (type A) has 50 layers with fixed thicknesses of 1.2 mm. The second collimator (type B) has 25 layers with a thickness of 1.0 mm on the object side and 25 layers with a thickness of 1.4 mm on the opposite side. The third collimator (type C) has 20 layers with non-uniform thicknesses. The ratios of the maximum artificial peak to the main-peak are calculated for point-source responses. The ratios for types A, B, and C collimators are 0.78, 0.08, and 0.03, respectively. The same performance for shielding undesirable gamma rays is achieved in the type C collimator as for a conventional collimator.