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We calculate the gravitational wave (GW) background spectra from kink propagation and kink-kink collisions on infinite cosmic superstrings. We take into account two characteristics of the cosmic superstring network: a small reconnection probability and Y-junctions. First, a small reconnection probability increases the number of infinite strings inside the horizon and enhances the kink production, which leads a larger amplitude of the GW background. Second, a kink going through a Y-junction transforms into three daughter kinks. In this way, the existence of Y-junctions also increases the number of kinks on cosmic superstrings. However, at the same time, it smooths out the sharpness of kinks rapidly and reduces the number of sharp kinks, which are responsible for the emissions of strong GW bursts. We compute the number distribution of kinks as a function of the sharpness by taking into account the above two effects, and translate it to the amplitude of the GW background spectra. We first investigate the case of the string network with equal string tensions, and find that the effect of Y-junctions to smooth out kink sharpness dominates that of the enhancement of the kink number by a small reconnection probability, and the GW amplitude turns out to be smaller than the ordinary cosmic string case. On the other hand, for non-equal string tensions, we find that there is a parameter space where the GW amplitude is slightly enhanced by the effect of a small reconnection probability.