The isotope shifts of the 6 $^{2}$${\mathit{S}}_{1/2}$--5 $^{2}$${\mathit{D}}_{5/2}$ transition in ${\mathrm{Ba}}^{+}$ have been measured using the high-resolution laser spectroscopy of a single trapped ion. The shifts are measured among three even ${\mathrm{Ba}}^{+}$ isotopes, $^{138}\mathrm{Ba}^{+}$, $^{136}\mathrm{Ba}^{+}$, and $^{134}\mathrm{Ba}^{+}$. The results are ${\ensuremath{\nu}}_{138\mathrm{\ensuremath{-}}}$${\ensuremath{\nu}}_{136}$=-106.143(4) MHz and ${\ensuremath{\nu}}_{138\mathrm{\ensuremath{-}}}$${\ensuremath{\nu}}_{134}$=-38.455(15) MHz. This experiment gives a measurement of isotope shifts for a heavy atom. The results should provide a stringent test for the theoretical calculations of the isotope shifts of alkali-metal-like atoms.