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The effects of the grain size of the doped SiC nanoparticles on the critical current density (Jc) of the Ti-sheathed MgB2 superconducting wires were studied. The concentration of the SiC dopant was 10% and the sizes of the SiC particles were 20 nm, 45 nm, and 123 nm. Contrary to the Jc results reported on the SiC-doped Fe-sheathed MgB2 wires, we found that the Jc for the Ti-sheathed MgB2 wires decreased with the size of the SiC particles. We also found that the Jc is greater than that of the undoped MgB2 wires only for the wires with 123 nm SiC size. This unusual dependence of Jc on the size of the SiC dopant is discussed in association with the results from the magnetization, electrical resistivity, x-ray diffraction, and transmission electron microscopy measurements.