The synthesis of well-defined four-armed star-shaped poly(butylene oxide) and figure-eight-shaped poly(butylene oxide)s (s-PBO and 8-PBO, respectively) with predicted molecular weights and narrow molecular weight distributions (Mw/Mns) was achieved by the t-Bu-P4-catalyzed ring-opening polymerization (ROP) of butylene oxide (BO). The t-Bu-P4-catalyzed ROP of BO using 1,2,4,5-benzenetetramethanol as the initiator produced s-PBOs having number-average molecular weights (Mn,NMRs) ranging from ca. 4000 to 12 000 g mol–1 and narrow Mw/Mns of <1.03. Cleavage of the linkage between the initiator residue and PBO arms in s-PBO provided evidence for the homogeneous growth of each arm during the polymerization. The synthesis of 8-PBO was carried out through three reaction steps including (1) the synthesis of a PBO possessing two azido groups at the chain center ((N3)2-(PBO)2) by the ROP of BO using 2,2-bis((6-azidohexyloxy)methy)propane-1,3-diol as the initiator, (2) the introduction of an ethynyl group at the two ω-chain ends by etherification using propargyl bromide to give the ω,ω′-diethynyl poly(butylene oxide) with two azido groups ((N3)2-(PBO-C≡CH)2), and (3) the intramolecular click cyclization of (N3)2-(PBO-C≡CH)2 using the copper(I) bromide/N,N,N′,N″,N″-pentamethyldiethylenetriamine catalyst in DMF under high dilution conditions. Size exclusion chromatography, FT-IR, and 1H NMR measurements confirmed that the click reaction proceeded in an intramolecular fashion to give 8-PBOs having Mn,NMRs ranging from ca. 3000 to 12 000 g mol–1 and narrow Mw/Mns of <1.06. The viscosity property of s-PBO and 8-PBO was evaluated together with linear and cyclic PBOs (l-PBO and c-PBO, respectively). The intrinsic viscosity ([η]) of l-PBO, c-PBO, s-PBO, and 8-PBO decreased in the order of l-PBO > s-PBO > c-PBO > 8-PBO.