The aim of this research is to carryout a design study on a variable geometry rectangular supersonic air-intake at different flight conditions. The design of the air-intake at supersonic Mach number according to “on-design” condition ( ), to get a maximum total-pressure recovery, and study the performance of air-intake at supersonic Mach number according to “off-design” conditions ( ). The air-intake consists of convergent-divergent nozzle. The number of oblique shock waves is induced by the sharp cowl lips at the nozzle entrance and their reflections may continue along the convergent passage depending on the free-stream Mach number and nozzle wall turning angle. The location of the normal shock wave is just downstream the throat, for an “off-design” condition, and at nozzle throat, at its “on-design” condition . The flow is assumed as one-dimensional compressible, and inviscid. The flow properties were calculated using the analytical method based on the relation of the oblique shock and normal shock waves. The divergent part was analyzed for different divergent lengths, to maintain the divergent angle less than value that causes flow separation and to get the maximum total pressure recovery. The convergent part was analyzed for different convergent lengths, to maintain the oblique shock and their reflected terminated before the throat position to get maximum total pressure recovery, .