A series of donors have been designed based on three building blocks, i.e., triphenylamine (TPA), 4,7-di(thiophen-2-yl)benzo-[c][1,2,5]thiadiazole (DBT), and oligothiophenes (5Th), to investigate suitable molecules toward solar cell materials. The donors are built by two donor fragments (TPA as D1 and 5Th as D2) and one acceptor fragment (DBT as A) in three topologies with or without linkages and electron-withdrawing groups. Their electronic and optical properties have been characterized by the PBE0/6-31G(d,p) and the TD-PBE0/6-31+G(d,p) approaches. The calculated results reveal that the asymmetric donor in the topology of D1-A-D2 with vinyl linkage and -NO2 groups is a rational strategy to design novel material possessing a small HOMO-LUMO gap, broad and intense absorption spectra, and higher charge transfer ability. The promising donors for [6,6]-phenyl-C-61-butyric acid methyl ester (PCBM), bisPCBM, and PC70BM. as acceptors are recommended theoretically for the first time for solar cells based on the proper match for frontier molecular orbitals between donors and acceptors.