Multiple variants of severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2) have spread around the world, but the neutralizing effects of antibodies induced by the existing vaccines have declined, which highlights the importance of developing vaccines against mutant virus strains. In this study, nine receptor-binding domain (RBD) proteins of the SARS-CoV-2 variants (B.1.1.7, B.1.351 and P.1 lineages) were constructed and fused with the Fc fragment of human IgG (RBD-Fc). These RBD-Fc proteins contained single or multiple amino acid substitutions at prevalent mutation points of spike protein, which enabled them to bind strongly to the polyclonal antibodies specific for wild-type RBD and to the recombinant human ACE2 protein. In the BALB/c, mice were immunized with the wild-type RBD-Fc protein first and boosted twice with the indicated mutant RBD-Fc proteins later. All mutant RBD-Fc proteins elicited high-level IgG antibodies and cross-neutralizing antibodies. The RBD-Fc proteins with multiple substitutions tended to induce higher antibody titers and neutralizing-antibody titers than the single-mutant RBD-Fc proteins. Meanwhile, both wild-type RBD-Fc protein and mutant RBD-Fc proteins induced significantly decreased neutralization capacity to the pseudovirus of B.1.351 and P.1 lineages than to the wild-type one. These data will facilitate the design and development of RBD-based subunit vaccines against SARS-COV-2 and its variants.