With medium wave infrared (MWIR) focal plane array-based (FPA) compressive imaging (CI), high-resolution images can be obtained with a low-resolution MWIR sensor. However, restricted by the size of digital micro-mirror devices (DMD), aperture interference is inevitable. According to the system model of FPA CI, aperture interference aggravates the blocky structural artifacts (BSA) in the reconstructed images, which reduces the image quality. In this paper, we propose a novel DMD mask design strategy, which can effectively suppress BSA and maximize the reconstruction efficiency. Compared with random binary codes, the storage space and computation cost can be significantly reduced. Based on the actual MWIR FPA CI system, we demonstrate the proposed DMD masks can effectively suppress the BSA in the reconstructed images. In addition, a new evaluation index, blocky root mean square error, is proposed to indicate the BSA in FPA CI.