One-dimensional (1D) π-d conjugated metal-organic frameworks (c-MOFs) have garnered widespread research interest in chemical energy storage and conversion. In this work, we introduce a universal principle to engineer the topological bands of 1D c-MOFs. Connected by d orbitals of transition metals, two equivalent hidden molecular π orbitals in 1D c-MOFs can generate a staggered hopping within and between the organic ligands, forming Su-Schrieffer-Heeger-shaped 1D topological bands. Guided by this discovery, we investigate the electronic structures of the typical 1D c-MOF assembled from Ni atoms and 2HQDI (QDI = 2,5-diamino-1,4-benzoquinonediimine) precursors (NiQDI) by first-principles calculations, revealing 1D topological bands around the Fermi level. Due to local bonding variations at the QDI terminations, these two hidden molecular π orbitals become atomically bonded but electronically separated at the edge QDI, creating spatially localized in-gap topological edge states at the end of the NiQDI chain. This definitive signature for 1D topological bands is identified through differential conductance spectra in scanning tunneling microscopy measurements. Our results provide conclusive experimental evidence for topological bands in 1D c-MOFs, paving the way for exploring the topological physics in organic materials through frontier molecular orbitals.