The B (2)Phi(5/2)-X(1) (2)Delta(3/2)(0,0) band at 778 nm and the C (2)Delta(3/2)-X(1) (2)Delta(3/2)(0,0) band at 737 nm of tantalum oxide (TaO) were recorded by laser excitation spectroscopy using a hollow cathode sputtering source to generate the molecules. The hyperfine structure arising from the (181)Ta (I=72) nucleus was measured at sub-Doppler resolution using the technique of intermodulated fluorescence spectroscopy. The hyperfine structure was assigned and fitted in order to derive accurate values for the magnetic dipole and electric quadrupole interactions. The magnetic hyperfine constant for the ground electronic state was also calculated using the density functional theory as h(3/2)=625 MHz, in good agreement with the experimental value of 647+/-10 MHz. This result suggests that the X (2)Delta ground state of TaO is well described by a pure deltasigma(2) electronic configuration, where the unpaired electron is located in a Ta 5ddelta orbital.