The optimum gains of a delay-and-sum microphone array for the near sound field, where the sound waves are spherical, have been investigated. The optimum gains give the highest signal-to-noise ratio in a sound field with background noise, and they give constant sensitivity to the sound source at every focal point. The optimum gains were theoretically derived as g[inf i]=C/r[inf i], where r[inf i] represents the distance between the array focal point and the ith microphone element and C represents the normalizing parameter that keeps the sound source sensitivity constant, independent of the focal point. Parameter C is a function of r[inf i] and r[inf c], where r[inf c] is the critical distance of the reverberant room. The results of computer simulation and indoor experiments (room volume: 83 m[sup 3], reverberation time: 0.2 s) showed a good array sensitivity distribution and power distribution estimation when each gain was optimized.