Previously we designed a dual-purpose multi-pinhole (MPH) collimator for improved clinical myocardial perfusion imaging (MPI) with extra capability of small animal imaging for a clinical gamma camera. However, the standard configuration for current clinical MPI is L-mode with two detectors ~90⁰ apart. This study aims to design a dual-head L-mode MPH collimator for potential stationary MPI based on a clinical SPECT/CT scanner. Two stationary L-mode configurations, L-mode-I/II, were proposed based on the work of Rittenbach et al. where the long axis of the left ventricle was perpendicular to either camera. With the pre-defined pinhole pattern with minimal projection truncation and <20% multiplexing, maximum packing density and detector usage, the optimized MPH collimator parameters including pinhole number, radius-of-rotation, collimator length, aperture size and acceptance angle were determined by maximizing the sensitivity based on the pre-determined field-of-view of 20 cm and target resolution of 1 cm, considering the physical constraints of L-mode-I/II. Analytical simulations using the 4D extended cardiac-torso phantom (XCAT) were performed for 4 selected MPH designs with superior sensitivity results. Noise-free and noisy projections were generated and reconstructed using 3D MPH OS-EM algorithm. Reconstructed images were evaluated by visual assessment, normalized-mean-square-error (NMSE) and normalized standard deviation (NSD). L-mode-II generally showed less NMSE as compared to L-mode-I. For L-mode-I, 11-pinhole had the best NMSE-NSD trade-off while for L-mode-II, 18-pinhole had the best trade-off. We concluded that stationary MPI acquisition by using a dual-head MPH collimator is feasible and has the potential for dynamic MPI.