Magnetic topological semimetals, a novel state of quantum matter with a nontrivial band topology, have emerged as a new frontier in physics and materials science. An external stimulus such as temperature or magnetic field could be expected to alter their spin states and thus Fermi surface anisotropies and topological features. Here, we perform angular magnetoresistance measurements and electronic band structure calculations to reveal the evolution of HoSb's Fermi surface anisotropies and topological nature in different magnetic states. The angular magnetoresistance results show that its Fermi surface anisotropy is robust in the paramagnetic state but is significantly modulated in the antiferromagnetic and ferromagnetic states. More interestingly, a transition from the trivial (nontrivial) to nontrivial (trivial) topological electronic phase is observed when HoSb undergoes a magnetic transition from the paramagnetic (antiferromagnetic) to antiferromagnetic (ferromagnetic) state induced by temperature (applied magnetic field). Our study suggests that HoSb provides an archetype platform to study the correlations between magnetism and topological states of matter. The topological nature of electronic states in HoSb significantly depends on spin orderings (NM, AFM or FM spin configuration). Only the electronic band structure in HoSb's antiferromagnetic state is confirmed to be topologically nontrivial.