Enhancement of spontaneous emission in a resonantBragg quantum well (QW) structure with 60 periods of triple InAs monolayers embedded in a GaAs matrix is studied experimentally and theoretically. From measurements of the time-resolved photoluminescence, besides the QW exciton at 1.47 eV, a specific super-radiant (SR) emission demonstrating nonlinear properties is found. The SR mode shows a near-quadratic dependence of intensity on excitation power, while its energy position follows the Bragg condition. It is revealed that the SR mode shows a peculiar non-monotonic dependence of intensity on direction, with a maximum observed at approximately 40°. The enhancement in the SR emission at a specific direction is correlated well with suggested theoretical consideration of the modal Purcell factor for periodic quantum well structures.