The B-cell antigen receptor (BCR) is composed of a membrane-bound immunoglobulin (mIg) of class M, D, G, A or E for antigen recognition and a disulfide-linked heterodimer between Igα and Igβ (Igα/β, also known as CD79A and CD79B) that functions as the signalling entity. The organizing principle of BCR assembly remains elusive. Here we report the cryo-electron microscopy structures of the intact IgM class BCR at 8.2 Å resolution and its Fab-deleted form (IgM BCRΔFab) at 3.6 Å resolution. At the ectodomain (ECD), Igα and Igβ position their respective Ig folds roughly in parallel with an approximate 2-fold symmetry, which is distinct from structures of Igβ/β homodimers. Unlike previous predictions, the BCR structure displays an asymmetric arrangement, in which the Igα/β ECD heterodimer mainly uses Igα to associate with Cμ3-Cμ4 domains of one heavy chain (μHC) while leaving the other heavy chain (μHC′) empty. The transmembrane domain (TMD) helices of the two μHCs also deviate from the 2-fold symmetry of the Cμ3-Cμ4 domain dimer and form together with the TMD helices of the Igα/β heterodimer a tight 4-helix bundle. The asymmetry at the TMD helices prevents the recruitment of two Igα/β heterodimers. Surprisingly, the connecting peptides (CPs) between the ECD and TMD are braided together through striking charge complementarity, resulting in intervening of the CP of μHC in between those of Igα and Igβ and crossover of the TMD relative to ECD for the Igα/β heterodimer, to guide the TMD assembly. Interfacial analyses suggest that the IgM BCR structure we present here may represent a general organizational architecture of all BCR classes. Our studies thus provide a structural platform for understanding B-cell signalling and for designing rational therapies against BCR-mediated diseases.