The competing magnetic ground states of the itinerant magnet EuCuSb, which has a hexagonal layered structure, were studied via magnetization, resistivity, and neutron-diffraction measurements on single-crystal samples. EuCuSb has a three-dimensional semimetallic band structure as confirmed by band calculation and angle-resolved photoelectron spectroscopy, consistent with the nearly isotropic metallic conductivity in the paramagnetic state. However, below the antiferromagnetic transition temperature of TN1 (8.5 K), the resistivity, especially along the hexagonal axis, increases significantly. This implies the emergence of anisotropic magnetic ordering coupled to the conducting electrons. Neutron-diffraction measurements show that the Eu spins, which order ferromagnetically within each layer, are collinearly modulated (up-up-down-down) along the hexagonal axis below TN1, followed by the partial emergence of helical spin modulation below TN2 (6 K). Based on the observation of anomalous magnetoresistance with hysteretic behavior, we discuss the competing nature of the ground state inherent in a frustrated Heisenberg-like spin system with a centrosymmetric structure.