A spontaneous exchange bias (SEB) discovered by Wang et al. [Phys. Rev. Lett. 106 (2011) 077203.] after zero-field cooling (ZFC) has attracted recent attention due to its interesting physics. In this letter, we report a giant SEB tuned by Sb-doping in Ni50Mn38Ga12-xSbx Heusler alloys. Such an SEB was switched on below the blocking temperature of approximately 50 K. The maximum exchange bias HE can arrive at 2930 Oe in a Ni50Mn38Ga10Sb2 sample after ZFC to 2 K. Further studies showed that this SEB was attributable to interaction of superspin glass (SSG) and antiferromagnetic matix, which was triggered by the crossover of SSG from canonical spin glass to a cluster spin glass. Our results not only explain the underlying physics of SEB, but also provide a way to tune and control the SEB performance.