Adopting the 3+1 neutrino mixing parameters by the IceCube and shortbase line experiments, we investigate the sterile-active neutrino oscillation effects on the supernova neutrino process. For the sterile neutrino ($ u_s$), we study two different luminosity models. First, we presume that the $ u_s$ does not interact with other particles through the standard interactions apart from the oscillation with the active neutrinos. Second, we consider that $ u_s$ can be directly produced by $ u_e$ scattering with matter. In both cases, we find that the pattern of neutrino oscillations can be changed drastically by the $ u_s$ in supernova environments. Especially multiple resonances occur, and consequently affect thermal neutrino-induced reaction rates. As a result, $^7$Li, $^7$Be, $^{11}$B, $^{11}$C, $^{92}$Nb, $^{98}$Tc and $^{138}$La yields in the $ u$-process are changed. Among those nuclei, $^7$Li and $^{11}$B yields can be constrained by the analysis of observed SiC X grains. Based on the meteoritic data, we conclude that the second model can be allowed while first model is excluded. The viability of the second model depends on the sterile neutrino temperature and the neutrino mass hierarchy.
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