A balloon-borne cosmic gamma-ray burst detection system has been designed for observation of small gamma-ray burst at a rate of better than one event per day and for determination of source locations. The detection system consists of four inclined large-area high pressure xenon counters. The source location is determined from counting differences between four xenon counters. The directional accuracy of the burst source depends on the gamma-ray burst size, the inclination of the four xenon counters and the elevation angle of the burst source. The relation between the burst detection frequency and the detector area is estimated for this design of the detection system.