Two field experiments were carried out at Research Farm of Alkod Station (Delta of Abyan) in 2012/2013 and 2013/2014 seasons to study the effect of plant density and intercropping pattern as well as their interaction on yield and competitive relationships of maize and cowpea. Four plant densities were used (56000, 67000, 83000 and 111000 plants /hectare) and three intercropping patterns (1:1, 2:1 and 3:3) for maize and cowpea respectively, in addition to sole cropping treatment. The results could be summarized as follows:   - Increasing plant density significantly increased biological and grain yield  of maize while harvest index was decreased. Intercropping patterns significantly reduced biological and grain yield of maize while harvest  index was increased. Interaction between plant densities and intercropping patterns significantly affected biological and grain yield of maize as well as harvest index and the maximum grain yield was obtained under 2:1 intercropping pattern at 83000 plants/ hectare.  - Biological and seed yield of cowpea were significantly increased by increasing plant density while harvest index was decreased with significant value in the second season. Intercropping patterns significantly reduced biological and seed yield while harvest index was increased. The interaction between plant densities and intercropping patterns had significant effect on biological and seed yield of cowpea in both seasons as well as harvest index in the second season and the highest seed yield was obtained under 3:3 patterns at 111000 plants/ hectare.  Land  equivalent  ratio( LER) and  relative  crowding  coefficient( K) values indicated that intercropping cowpea with maize gave yield advantage at all combinations of plant densities and intercropping patterns and the highest values of LER (1.51 and 160) in the first and second seasons respectively were obtained under 3:3 pattern at 111000 plants/ hectare.  - Aggressivity values and competitive ratio indicated that maize was the dominant intercrop while cowpea was the dominated intercrop.