We calculate and measure the magic wavelengths for the 6s(2) S-1(0)-6s6p P-3(1) intercombination transition of the neutral ytterbium atom. The calculation is performed with the ab initio configuration interaction + all-order method. The measurement is done with laser spectroscopy on cold atoms in an optical dipole trap. The magic wavelengths are determined to be 1035.68(4) nm for the pi transition (Delta m = 0) and 1036.12(3) nm for the sigma transitions (vertical bar Delta m vertical bar = 1) in agreement with the calculated values. Laser cooling on the narrow intercombination transition could achieve better results for atoms in an optical dipole trap when the trap wavelength is tuned to near the magic wavelength.