Advances in basic and applied research of conventional grating have been attracting much attention from optical engineering community. However, the higher orders diffraction contamination degrades the spectral purity obtained by conventional gratings seriously. Many designs of single-order or quasi-single-order gratings have been proposed to suppress higher-order diffraction contributions, however, their inhibitive effects on the higher order diffractions are restrained by the processing accuracy unavoidably. In this paper, we propose a grating that incorporates a quasi-periodical array of rectangular holes, and achieves larger tolerance of processing errors compared with the previously designed gratings by optimizing the probability density distribution function of the holes. This paper describes an analytical study of the diffraction property of this grating. Theoretical calculations reveal that the grating completely suppresses the 2^nd, 3^rd, and 4^th orders diffractions, and the ratio of the 5^th order diffraction efficiency to that of the 1^st is as low as 0.01% even if relative errors for hole sizes exceed 20%, which greatly decreases the required processing accuracy.