The wide transmission and host adaptation of SARS-CoV-2 have led to the rapid accumulation of mutations, posing significant challenges to the effectiveness of vaccines and therapeutic antibodies. Although several neutralizing antibodies were authorized for emergency clinical use, natural antibodies isolated from convalescent patients are vulnerable to SARS-CoV-2 Spike mutations. Here, we describe the screen of a panel of SARS-CoV-2 receptor-binding domain (RBD) targeted nanobodies (Nbs) from a synthetic library and the design of a biparatopic Nb dimer, named Nb1-Nb2, with tight affinity and super wide neutralization breadth against multiple SARS-CoV-2 variants of concern or interest. Deep-mutational scanning experiments identify the potential binding epitopes of the monomeric Nb1 and Nb2 on the RBD and demonstrate that bivalent Nb1-Nb2 has a strong escape resistant feature against more than 60 tested RBD amino acid substitutions. Using pseudovirion-based and trans-complementation SARS-CoV-2 tools, we determine that Nb1-Nb2 broadly neutralizes SARS-CoV-2, including variants Alpha (B.1.1.7), Beta (B.1.351), Gamma (P.1), Delta (B.1.617.2), Lambda (C.37), Kappa (B.1.617.1) and Mu (B.1.621). Furthermore, a heavy chain antibody is constructed by fusing the human IgG1 Fc to the biparatopic Nb (designated as Nb1-Nb2-Fc) to improve its neutralization potency, yield, stability and potential half-life extension. For the new Omicron variant (B.1.1.529) that harbors unprecedented multiple RBD mutations, Nb1-Nb2-Fc keeps a firm affinity (KD < 1.0*10E-12 M) and neutralizing activity (IC50 = 0.0017 nM). Together, we developed a biparatopic human heavy chain antibody with ultrapotent and broad-spectrum SARS-CoV-2 neutralization activity which highlights the potential clinical applications.