Jungle Strike features two antagonists: Ibn Kilbaba, the son of Desert Strike's antagonist, and Carlos Ortega, a notorious South American drug lord. The opening sequence depicts the two men observing a nuclear explosion on a deserted island, while discussing the delivery of "nuclear resources" and an attack on Washington D.C.; Kilbaba seeks revenge for his father's death at the hands of the US, while Ortega wishes to "teach the Yankees to stay out of my drug trade".

The player takes control of a "lone special forces" pilot. The game's first level depicts the protagonist repelling terrorist attacks on Washington, D.C., including the President's limousine. Subsequent levels depict counter-attacks on the drug lord's forces, progressing towards his "jungle fortress". In the game's penultimate level, the player pursues Kilbaba and Ortega to their respective hideouts before capturing them.