It is well known that narrow beams are produced for maximum directivity, small beam width from a line source of specified length meeting desired side-lobe levels. However, side-lobe suppression may not be required in all the directions for certain applications. The generated patterns are useful for point to point communication and high resolution radars, but they have limited use in the marine radars where pitch and roll of the ship exists. There are some situations where the array associated with the radar operating from a ship requires asymmetric Sum and Difference patterns to take care of pitch and roll of the ship in turbulent seas. This particular application demands the generation of patterns with asymmetrical side-lobes adjacent to the main lobe. These patterns are characterized by one main lobe and with low side-lobes on one side and high side-lobes on the other side of the main beam. In order to meet the EMI standards the side-lobe levels of the radiation beams are made smaller and smaller. The side-lobe levels of the order -25 dB are acceptable in general. If further lower side-lobes are required, it is practically very difficult to design appropriate tapered excitations. In view of the above facts some investigations are carried out in the present work on the design of line sources, to generate asymmetrical patterns to make them suitable in marine radars applications. The antennas associated with the marine radars are required to produce patterns with asymmetric side- lobes. In particular the side-lobes in one side are lower than those of the other side. The amplitude and phase distributions are designed for small and large arrays. The radiation patterns are numerically computed and they are presented in u- domain.