This paper presents the analysis and design of a reflection-cancelling transverse slot-pair array antenna with baffles by using the Spectrum of Two-Dimensional Solutions (S2DS) method. For the transverse slot array, the slot spacings with more than one free-space wavelength cause the grating-lobes. The baffles suppress the grating-lobes effectively. A one-dimensional slot array is extracted from the 2D array with in-phase excitation by assuming periodicity in the transversal direction. The uniform excitation over the finite array is synthesized iteratively to demonstrate the fast and accurate results by S2DS. A unit design model with the baffles is introduced to determine the initial parameters of the slot-pairs, which greatly accelerate the iterations process. Experiments at 25.3GHz demonstrate the suppression of the grating lobes to the level less than -20.0dB and also the good uniformity of the aperture field distribution.