We present a theoretical study on a series of novel organometallic sandwich molecular wires (SMWs), which are constructed with alternating iron atoms and cyclopentadienyl (Cp) rings, using DFT and nonequilibrium Green's function techniques. It is found that that the SMWs are stable, flexible structures having half-metallic (HM) properties with 100% negative spin polarization near the Fermi level in the ground state. Some SMWs of finite size show a nearly perfect spin filter effect (SFE) when coupled between ferromagnetic electrodes. Moreover, their I-V curves exhibit negative differential resistance (NDR), which is essential for certain electronic applications. The SMWs are the first linear molecules with HM, high SFE, and NDR and can be easily synthesized. In addition, we also analyze the underlying mechanisms via the transmission spectra and spin-dependent calculations. These findings strongly suggest that the SMWs are promising materials for application in molecular electronics.