A linear cascade experimental apparatus often consists of only a few cascade blades. Advantages to this experimental arrangement are increased by the use of larger cascade blades, a lower mass flow rate, a corresponding decrease in required power, and easier optical access within the cascade passage. However, fewer cascade blades in the cascade row make it difficult to establish periodic flow conditions between blades compared to infinite cascade model experiments. Generally, removing fluid from the cascade walls or adjusting tailboards located downstream of the cascade are common methods to establish periodic flow conditions through the cascade blades. In this study, a passage for cascade experiments is designed to satisfy infinite cascade flow conditions without any flow control or tailboards. A one-pitch at cascade row is adopted as its width and only a single cascade blade is installed within the passage. The surface isentropic Mach number distribution on the blade is chosen for the existence of infinite cascade flow conditions, and 14 geometric design variables related to the passage shape are applied to the design of a one-pitch passage by using a genetic algorithm. Flow structures within a passage designed using a genetic algorithm match with those obtained with the infinite cascade flow condition. Computed results obtained with a single cascade blade show that infinite cascade flow conditions can be obtained by modifying only the passage walls of the cascade experimental apparatus.