In materials showing a linear magnetoelectric (ME) effect, unconventional functionalities can be anticipated such as electric control of magnetism and nonreciprocal optical responses. Thus, the search for new linear ME materials is of interest in materials science. Here, using a recently proposed design principle of linear ME materials, which is based on the combination of local structural asymmetry and collinear antiferromagnetism, we demonstrate that an anion-deficient fluorite derivative, Mn3Ta2O8, is a new linear ME material. This is evidenced by the onset of magnetic-field-induced electric polarization in its collinear antiferromagnetic phase below TN = 24 K. Furthermore, we also find an antiferroelectric-like phase transition at TS = 55 K, which is attributable to an off-center displacement of magnetic Mn2+ ions. The present study shows that Mn3Ta2O8 is a rare material that exhibits both ME and antiferroelectric-like transitions. Thus, Mn3Ta2O8 may provide an opportunity to investigate the physics associated with complicated interactions between magnetic (spin) and electric dipole degrees of freedom.