The catalytic conversion of ortho-hydrogen (o-H2) to para-hydrogen (p-H2) serves as a crucial step in the storage of liquid hydrogen. A variety of iron-cobalt bimetallic catalysts (FCO) were synthesized using a precipitation method, incorporating diverse levels of Co doping into Fe-based catalysts. The effects of Co doping on the crystal structure, porosity, and magnetism of FCO catalysts were studied by XRD, N2 physical adsorption, FTIR, XPS, and VSM analyses. The efficiency of ortho-para hydrogen conversion over FCO at 77 K was evaluated. It was found that the catalyst’s lag coefficient was significantly improved by Co doping, leading to an increase of magnetic moment. The catalyst of FCO-5 with a Fe/(Fe + Co) molar ratio of 0.5 exhibited the highest activity in ortho-para hydrogen conversion. The corresponding conversion rate, outlet p-H2 content, and the reaction rate constant were 99.2%, 49.7% and 291.7 mol·L−1·s−1, respectively, under a gas hourly space velocity of 5400 h−1.