The low-temperature magnetic properties of LaCoGe with the tetragonal CeFeSi-type structure were investigated by Co-59- and La-139-nuclear magnetic resonance (NMR) and nuclear quadrupole resonance (NQR) measurements. The nuclear spin lattice relaxation rate divided by the temperature, 1/(T1T), gradually increases with decreasing temperature and shows a kink at approximately 18 K, below which an inhomogeneous internal field appears at the Co nuclear site. These results indicate that antiferromagnetic ordering occurs below T-N similar to 18 K. However, an internal field was not observed at the La nuclear site below TN. Taking all NMR results into account, we conclude that spin-density-wave (SDW)-type ordering occurs, where magnetic correlations are of the checkerboard type [Q = (pi, pi)] in the ab-plane and have a long periodicity along the c-axis with inhomogeneous ordered moments pointing to the c-axis.