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Small-angle differential cross sections of proton elastic scattering off 78 Kr with a collision energy of 152.7 MeV/u were measured at the experimental Cooler Storage Ring of the Heavy Ion Research Facility in Lanzhou (HIRFL-CSR). Low energy recoil protons from the elastic scattering were counted by a silicon-strip detector to determine relative differential cross sections. A model-dependent root-mean-square matter radius of 4.16(12) fm for the 78 Kr nucleus was deduced by employing the Glauber model. Compared to the proton radius of 4.13 fm for 78 Kr, our center value of matter radius is slightly larger. This finding in 78 Kr is opposite to the known results of 76,80 Kr, where the matter radii are smaller than the corresponding proton radii. However, considering the relatively large radius error of 78 Kr, the difference is not statistically significant, and further experiments are necessary.