SrHo 2O 4 is a geometrically frustrated magnet in which the magnetic Ho 3 + ions are connected through a network of zigzag chains and coupled by several competing interactions. The Ho 3 + ions show a pronounced Ising anisotropy at low temperatures, and the spins on the two crystallographically inequivalent magnetic sites point along orthogonal crystallographic axes. Using single-crystal neutron diffraction, we report on the development of complex and highly anisotropic short- and long-range magnetic order in SrHo 2O 4 induced by an applied magnetic field. For H ‖ c , the diffuse scattering around the k = 0 positions is suppressed and above 0.5 T the spin structure for one of the Ho sites is long-range and ferromagnetic. For H ‖ b , planes of diffuse scattering at Q = ( h k ± l 2 ) are split by the field, and an up–up–down magnetic order associated with a 1/3-magnetisation plateau develops at 0.8 T. Further increasing the field above 1.2 T allows the second Ho site to also order in a long-range ferromagnetic structure.